Bessel-function-calling-conventions.html 7.6 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164
  1. <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html401/loose.dtd">
  2. <html>
  3. <!-- Created on November 8, 2012 by texi2html 1.82
  4. texi2html was written by:
  5. Lionel Cons <[email protected]> (original author)
  6. Karl Berry <[email protected]>
  7. Olaf Bachmann <[email protected]>
  8. and many others.
  9. Maintained by: Many creative people.
  10. Send bugs and suggestions to <[email protected]>
  11. -->
  12. <head>
  13. <title>avram - a virtual machine code interpreter: D.1.1 Bessel function calling conventions</title>
  14. <meta name="description" content="avram - a virtual machine code interpreter: D.1.1 Bessel function calling conventions">
  15. <meta name="keywords" content="avram - a virtual machine code interpreter: D.1.1 Bessel function calling conventions">
  16. <meta name="resource-type" content="document">
  17. <meta name="distribution" content="global">
  18. <meta name="Generator" content="texi2html 1.82">
  19. <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
  20. <style type="text/css">
  21. <!--
  22. a.summary-letter {text-decoration: none}
  23. blockquote.smallquotation {font-size: smaller}
  24. pre.display {font-family: serif}
  25. pre.format {font-family: serif}
  26. pre.menu-comment {font-family: serif}
  27. pre.menu-preformatted {font-family: serif}
  28. pre.smalldisplay {font-family: serif; font-size: smaller}
  29. pre.smallexample {font-size: smaller}
  30. pre.smallformat {font-family: serif; font-size: smaller}
  31. pre.smalllisp {font-size: smaller}
  32. span.roman {font-family:serif; font-weight:normal;}
  33. span.sansserif {font-family:sans-serif; font-weight:normal;}
  34. ul.toc {list-style: none}
  35. -->
  36. </style>
  37. </head>
  38. <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
  39. <a name="Bessel-function-calling-conventions"></a>
  40. <table cellpadding="1" cellspacing="1" border="0">
  41. <tr><td valign="middle" align="left">[<a href="bes.html#bes" title="Previous section in reading order"> &lt; </a>]</td>
  42. <td valign="middle" align="left">[<a href="Bessel-function-errors.html#Bessel-function-errors" title="Next section in reading order"> &gt; </a>]</td>
  43. <td valign="middle" align="left"> &nbsp; </td>
  44. <td valign="middle" align="left">[<a href="External-Libraries.html#External-Libraries" title="Beginning of this chapter or previous chapter"> &lt;&lt; </a>]</td>
  45. <td valign="middle" align="left">[<a href="bes.html#bes" title="Up section"> Up </a>]</td>
  46. <td valign="middle" align="left">[<a href="Copying.html#Copying" title="Next chapter"> &gt;&gt; </a>]</td>
  47. <td valign="middle" align="left"> &nbsp; </td>
  48. <td valign="middle" align="left"> &nbsp; </td>
  49. <td valign="middle" align="left"> &nbsp; </td>
  50. <td valign="middle" align="left"> &nbsp; </td>
  51. <td valign="middle" align="left">[<a href="avram.html#Top" title="Cover (top) of document">Top</a>]</td>
  52. <td valign="middle" align="left">[<a href="avram_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>
  53. <td valign="middle" align="left">[<a href="Function-Index.html#Function-Index" title="Index">Index</a>]</td>
  54. <td valign="middle" align="left">[<a href="avram_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
  55. </tr></table>
  56. <hr size="1">
  57. <a name="Bessel-function-calling-conventions-1"></a>
  58. <h3 class="subsection">D.1.1 Bessel function calling conventions</h3>
  59. <a name="index-bessel-functions"></a>
  60. <p>The virtual code interface simplifies the gsl C language API by
  61. excluding the facilities for error estimates, omitting certain array
  62. valued functions, and subsuming sets of related functions
  63. within common ones where possible.
  64. </p>
  65. <p>The functions with names in the following group take an argument of
  66. the form <code>(n,x)</code>, where <code>n</code> identifies the member of the
  67. function family, and <code>x</code> is the argument to the function.
  68. </p>
  69. <ul>
  70. <li> <code>J</code>
  71. regular cylindrical Bessel functions
  72. </li><li> <code>Y</code>
  73. irregular cylindrical Bessel functions
  74. </li><li> <code>I</code>
  75. regular modified cylindrical Bessel functions
  76. </li><li> <code>K</code>
  77. irregular modified cylindrical Bessel functions
  78. </li></ul>
  79. <p>For these functions, <code>n</code> can be either a natural number encoded
  80. as in <a href="Representation-of-Numeric-and-Textual-Data.html#Representation-of-Numeric-and-Textual-Data">Representation of Numeric and Textual Data</a>, or a floating
  81. point number encoded as in <a href="math.html#math"><code>math</code></a>. The latter case specifies
  82. functions of a fractional order. The relevant gsl function is called
  83. based on the value and type of the parameter.
  84. </p>
  85. <p>Two further related families of functions follow the same calling
  86. convention.
  87. </p>
  88. <ul>
  89. <li> <code>Isc</code>
  90. scaled regular modified cylindrical Bessel functions
  91. </li><li> <code>Ksc</code>
  92. scaled irregular modified cylindrical Bessel functions
  93. </li></ul>
  94. <p>The foregoing functions are related to those above by an exponential scale
  95. factor as documented in the gsl reference manual.
  96. </p>
  97. <p>Functions with names in the following group also take an argument of
  98. the form <code>(n,x)</code>, but are not defined for fractional orders and
  99. so require a natural number for <code>n</code>.
  100. </p>
  101. <ul>
  102. <li> <code>j</code>
  103. regular spherical Bessel functions
  104. </li><li> <code>y</code>
  105. irregular spherical Bessel functions
  106. </li><li> <code>isc</code>
  107. regular modified spherical Bessel functions
  108. </li><li> <code>ksc</code>
  109. irregular modified spherical Bessel functions
  110. </li></ul>
  111. <p>The functions in the remaining group follow idiosyncratic calling
  112. conventions.
  113. </p>
  114. <ul>
  115. <li> <code>zJ0</code>, <code>zJ1</code>
  116. These take a natural number <code>n</code> and return the <code>n</code>th root of
  117. the regular cylindrical Bessel functions of order 0 or 1,
  118. respectively.
  119. </li><li> <code>zJnu</code>
  120. This takes a pair <code>(nu,n)</code> where <code>nu</code> is the (fractional)
  121. order of a regular cylindrical Bessel function, <code>n</code> is a natural
  122. number. It returns the <code>n</code>th zero of the function.
  123. </li><li> <code>lnKnu</code>
  124. This takes a pair of floating point numbers <code>(nu,x)</code> where
  125. <code>nu</code> is the (fractional) order of an irregular modified
  126. cylindrical Bessel and <code>x</code> is the argument to the function,
  127. and it returns the natural log of the function.
  128. </li></ul>
  129. <hr size="1">
  130. <table cellpadding="1" cellspacing="1" border="0">
  131. <tr><td valign="middle" align="left">[<a href="bes.html#bes" title="Previous section in reading order"> &lt; </a>]</td>
  132. <td valign="middle" align="left">[<a href="Bessel-function-errors.html#Bessel-function-errors" title="Next section in reading order"> &gt; </a>]</td>
  133. <td valign="middle" align="left"> &nbsp; </td>
  134. <td valign="middle" align="left">[<a href="External-Libraries.html#External-Libraries" title="Beginning of this chapter or previous chapter"> &lt;&lt; </a>]</td>
  135. <td valign="middle" align="left">[<a href="bes.html#bes" title="Up section"> Up </a>]</td>
  136. <td valign="middle" align="left">[<a href="Copying.html#Copying" title="Next chapter"> &gt;&gt; </a>]</td>
  137. <td valign="middle" align="left"> &nbsp; </td>
  138. <td valign="middle" align="left"> &nbsp; </td>
  139. <td valign="middle" align="left"> &nbsp; </td>
  140. <td valign="middle" align="left"> &nbsp; </td>
  141. <td valign="middle" align="left">[<a href="avram.html#Top" title="Cover (top) of document">Top</a>]</td>
  142. <td valign="middle" align="left">[<a href="avram_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>
  143. <td valign="middle" align="left">[<a href="Function-Index.html#Function-Index" title="Index">Index</a>]</td>
  144. <td valign="middle" align="left">[<a href="avram_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
  145. </tr></table>
  146. <p>
  147. <font size="-1">
  148. This document was generated on <i>November 8, 2012</i> using <a href="http://www.nongnu.org/texi2html/"><i>texi2html 1.82</i></a>.
  149. </font>
  150. <br>
  151. </p>
  152. </body>
  153. </html>