diff options
Diffstat (limited to 'libs/math/doc/html/math_toolkit/bessel')
6 files changed, 78 insertions, 78 deletions
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html b/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html index 16f0bdac4..3515bf781 100644 --- a/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html +++ b/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Derivatives of the Bessel Functions</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../bessel.html" title="Bessel Functions"> <link rel="prev" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds"> <link rel="next" href="../hankel.html" title="Hankel Functions"> @@ -119,19 +119,19 @@ In the general case, the derivatives are calculated using the relations: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives1.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives1.svg"></span> </p> <p> There are also a number of special cases, for large x we have: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives4.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives4.svg"></span> </p> <p> And for small x: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives5.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives5.svg"></span> </p> </div> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_first.html b/libs/math/doc/html/math_toolkit/bessel/bessel_first.html index 1d99d2199..31ad8bae6 100644 --- a/libs/math/doc/html/math_toolkit/bessel/bessel_first.html +++ b/libs/math/doc/html/math_toolkit/bessel/bessel_first.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Bessel Functions of the First and Second Kinds</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../bessel.html" title="Bessel Functions"> <link rel="prev" href="bessel_over.html" title="Bessel Function Overview"> <link rel="next" href="bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"> @@ -65,10 +65,10 @@ where: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel2.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel3.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel3.svg"></span> </p> <p> The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result @@ -98,14 +98,14 @@ The following graph illustrates the cyclic nature of J<sub>v</sub>: </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_j.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_j.svg" align="middle"></span> </p> <p> The following graph shows the behaviour of Y<sub>v</sub>: this is also cyclic for large <span class="emphasis"><em>x</em></span>, but tends to -∞   for small <span class="emphasis"><em>x</em></span>: </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/cyl_neumann.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/cyl_neumann.svg" align="middle"></span> </p> <h5> <a name="math_toolkit.bessel.bessel_first.h2"></a> @@ -509,10 +509,10 @@ can be used to move to <span class="emphasis"><em>v > 0</em></span>: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel9.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel9.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel10.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel10.svg"></span> </p> <p> Note that if the order is an integer, then these formulae reduce to: @@ -566,16 +566,16 @@ and <a href="http://functions.wolfram.com/03.03.06.0040.01" target="_top">http://functions.wolfram.com/03.03.06.0040.01</a>): </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel_y0_small_z.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel_y0_small_z.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel_y1_small_z.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel_y1_small_z.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel_y2_small_z.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel_y2_small_z.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel_yn_small_z.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel_yn_small_z.svg"></span> </p> <p> When <span class="emphasis"><em>x</em></span> is small compared to <span class="emphasis"><em>v</em></span> and @@ -584,14 +584,14 @@ often too slow to converge to be used (see <a href="http://functions.wolfram.com/03.03.06.0034.01" target="_top">http://functions.wolfram.com/03.03.06.0034.01</a>): </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel_yv_small_z.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel_yv_small_z.svg"></span> </p> <p> When <span class="emphasis"><em>x</em></span> is small compared to <span class="emphasis"><em>v</em></span>, J<sub>v</sub>x   is best computed directly from the series: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel2.svg"></span> </p> <p> In the general case we compute J<sub>v</sub>   and Y<sub>v</sub>   simultaneously. @@ -606,13 +606,13 @@ as well as the Wronskian: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel8.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel8.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel11.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel11.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel12.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel12.svg"></span> </p> <p> See: F.S. Acton, <span class="emphasis"><em>Numerical Methods that Work</em></span>, The Mathematical @@ -639,13 +639,13 @@ J<sub>μ</sub>, J<sub>μ+1</sub>, Y<sub>μ</sub>, Y<sub>μ+1</sub> can be calculated by </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel13.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel13.svg"></span> </p> <p> where </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel14.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel14.svg"></span> </p> <p> J<sub>ν</sub> and Y<sub>μ</sub> are then calculated using backward (Miller's algorithm) and forward @@ -657,13 +657,13 @@ series: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel15.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel15.svg"></span> </p> <p> where </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel16.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel16.svg"></span> </p> <p> g<sub>k</sub>   and h<sub>k</sub>   diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_over.html b/libs/math/doc/html/math_toolkit/bessel/bessel_over.html index 8896253ff..a85b80769 100644 --- a/libs/math/doc/html/math_toolkit/bessel/bessel_over.html +++ b/libs/math/doc/html/math_toolkit/bessel/bessel_over.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Bessel Function Overview</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../bessel.html" title="Bessel Functions"> <link rel="prev" href="../bessel.html" title="Bessel Functions"> <link rel="next" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds"> @@ -35,7 +35,7 @@ Bessel Functions are solutions to Bessel's ordinary differential equation: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel1.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel1.svg"></span> </p> <p> where ν   is the <span class="emphasis"><em>order</em></span> of the equation, and may be an arbitrary @@ -51,7 +51,7 @@ and known as a Bessel function of the first kind: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel2.svg"></span> </p> <p> This function is implemented in this library as <a class="link" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>. @@ -62,7 +62,7 @@ and is known as either a Bessel Function of the second kind, or as a Neumann function: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel3.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel3.svg"></span> </p> <p> This function is implemented in this library as <a class="link" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>. @@ -71,34 +71,34 @@ and is known as either a Bessel The Bessel functions satisfy the recurrence relations: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel4.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel4.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel5.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel5.svg"></span> </p> <p> Have the derivatives: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel6.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel6.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel7.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel7.svg"></span> </p> <p> Have the Wronskian relation: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel8.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel8.svg"></span> </p> <p> and the reflection formulae: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel9.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel9.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/bessel10.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/bessel10.svg"></span> </p> <h5> <a name="math_toolkit.bessel.bessel_over.h1"></a> @@ -112,7 +112,7 @@ and is known as either a Bessel are the two linearly independent solutions to the modified Bessel equation: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel1.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel1.svg"></span> </p> <p> The solutions are known as the modified Bessel functions of the first and @@ -121,10 +121,10 @@ and is known as either a Bessel respectively: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel2.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel3.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel3.svg"></span> </p> <p> These functions are implemented in this library as <a class="link" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a> @@ -134,34 +134,34 @@ respectively: The modified Bessel functions satisfy the recurrence relations: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel4.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel4.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel5.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel5.svg"></span> </p> <p> Have the derivatives: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel6.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel6.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel7.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel7.svg"></span> </p> <p> Have the Wronskian relation: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel8.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel8.svg"></span> </p> <p> and the reflection formulae: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel9.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel9.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel10.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel10.svg"></span> </p> <h5> <a name="math_toolkit.bessel.bessel_over.h2"></a> @@ -173,7 +173,7 @@ respectively: of variables, the radial equation has the form: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/sbessel1.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/sbessel1.svg"></span> </p> <p> The two linearly independent solutions to this equation are called the spherical @@ -181,7 +181,7 @@ respectively: J<sub>n</sub>   and Y<sub>n</sub>   by: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/sbessel2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/sbessel2.svg"></span> </p> <p> The spherical Bessel function of the second kind y<sub>n</sub>   diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_root.html b/libs/math/doc/html/math_toolkit/bessel/bessel_root.html index 63ac4464a..45babf62f 100644 --- a/libs/math/doc/html/math_toolkit/bessel/bessel_root.html +++ b/libs/math/doc/html/math_toolkit/bessel/bessel_root.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Finding Zeros of Bessel Functions of the First and Second Kinds</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../bessel.html" title="Bessel Functions"> <link rel="prev" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds"> <link rel="next" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds"> @@ -159,10 +159,10 @@ nor NaN. </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/bessel_j_zeros.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/bessel_j_zeros.svg" align="middle"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/neumann_y_zeros.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/neumann_y_zeros.svg" align="middle"></span> </p> <h5> <a name="math_toolkit.bessel.bessel_root.h2"></a> diff --git a/libs/math/doc/html/math_toolkit/bessel/mbessel.html b/libs/math/doc/html/math_toolkit/bessel/mbessel.html index ad62070e8..23c042376 100644 --- a/libs/math/doc/html/math_toolkit/bessel/mbessel.html +++ b/libs/math/doc/html/math_toolkit/bessel/mbessel.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Modified Bessel Functions of the First and Second Kinds</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../bessel.html" title="Bessel Functions"> <link rel="prev" href="bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"> <link rel="next" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds"> @@ -66,10 +66,10 @@ where: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel2.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel3.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel3.svg"></span> </p> <p> The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result @@ -99,13 +99,13 @@ The following graph illustrates the exponential behaviour of I<sub>v</sub>. </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_i.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_i.svg" align="middle"></span> </p> <p> The following graph illustrates the exponential decay of K<sub>v</sub>. </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_k.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_k.svg" align="middle"></span> </p> <h5> <a name="math_toolkit.bessel.mbessel.h2"></a> @@ -365,7 +365,7 @@ the recurrence relation: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel5.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel5.svg"></span> </p> <p> starting from K<sub>0</sub>   and K<sub>1</sub>   which are calculated using rational the approximations @@ -377,17 +377,17 @@ I<sub>v</sub>x   is best computed directly from the series: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel17.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel17.svg"></span> </p> <p> In the general case, we first normalize ν   to [<code class="literal">0, [inf]</code>) with the help of the reflection formulae: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel9.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel9.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel10.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel10.svg"></span> </p> <p> Let μ   = ν - floor(ν + 1/2), then μ   is the fractional part of ν   such that |μ| <= 1/2 @@ -401,13 +401,13 @@ fractions as well as the Wronskian: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel11.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel11.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel12.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel12.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel8.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel8.svg"></span> </p> <p> The continued fractions are computed using the modified Lentz's method (W.J. @@ -431,13 +431,13 @@ can be calculated by </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel13.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel13.svg"></span> </p> <p> where </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel14.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel14.svg"></span> </p> <p> <span class="emphasis"><em>S</em></span> is also a series that is summed along with CF2, see @@ -451,13 +451,13 @@ can be calculated by series: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel15.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel15.svg"></span> </p> <p> where </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/mbessel16.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/mbessel16.svg"></span> </p> <p> f<sub>k</sub>   and h<sub>k</sub>   diff --git a/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html b/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html index 482154504..9d36025a2 100644 --- a/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html +++ b/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Spherical Bessel Functions of the First and Second Kinds</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../bessel.html" title="Bessel Functions"> <link rel="prev" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds"> <link rel="next" href="bessel_derivatives.html" title="Derivatives of the Bessel Functions"> @@ -66,7 +66,7 @@ where: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/sbessel2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/sbessel2.svg"></span> </p> <p> The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result @@ -86,14 +86,14 @@ The j<sub>v</sub>   function is cyclic like J<sub>v</sub>   but differs in its behaviour at the origin: </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/sph_bessel.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/sph_bessel.svg" align="middle"></span> </p> <p> Likewise y<sub>v</sub>   is also cyclic for large x, but tends to -∞   for small <span class="emphasis"><em>x</em></span>: </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/sph_neumann.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/sph_neumann.svg" align="middle"></span> </p> <h5> <a name="math_toolkit.bessel.sph_bessel.h2"></a> @@ -123,7 +123,7 @@ for small <span class="emphasis"><em>x</em></span>: implemented directly in terms of their definitions: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/sbessel2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/sbessel2.svg"></span> </p> <p> The special cases occur for: @@ -136,7 +136,7 @@ for small <span class="emphasis"><em>x</em></span>: and for small <span class="emphasis"><em>x < 1</em></span>, we can use the series: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/sbessel5.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/sbessel5.svg"></span> </p> <p> which neatly avoids the problem of calculating 0/0 that can occur with the |