Página inicial Explorar Ajuda
Registrar Entrar
devn00b
/
EQ2EMu
9
3
Fork 0
Arquivos Issues 69 Pull Requests 0 Wiki
Tree: 231c866c2c
Branches Tags
EQ2EMu
/
EQ2
/
source
/
depends
/
boost_1_72_0
/
libs
/
math
/
doc
/
html
/
special.html

special.html 16 KB
Histórico Raw

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240 
  1. <html>
    2. 

  2. <head>
    3. 

  3. <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
    4. 

  4. <title>Chapter&#160;8.&#160;Special Functions</title>
    5. 

  5. <link rel="stylesheet" href="math.css" type="text/css">
    6. 

  6. <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
    7. 

  7. <link rel="home" href="index.html" title="Math Toolkit 2.11.0">
    8. 

  8. <link rel="up" href="index.html" title="Math Toolkit 2.11.0">
    9. 

  9. <link rel="prev" href="math_toolkit/norms.html" title="Norms">
    10. 

  10. <link rel="next" href="math_toolkit/number_series.html" title="Number Series">
    11. 

  11. </head>
    12. 

  12. <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
    13. 

  13. <table cellpadding="2" width="100%"><tr>
    14. 

  14. <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
    15. 

  15. <td align="center"><a href="../../../../index.html">Home</a></td>
    16. 

  16. <td align="center"><a href="../../../../libs/libraries.htm">Libraries</a></td>
    17. 

  17. <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
    18. 

  18. <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
    19. 

  19. <td align="center"><a href="../../../../more/index.htm">More</a></td>
    20. 

  20. </tr></table>
    21. 

  21. <hr>
    22. 

  22. <div class="spirit-nav">
    23. 

  23. <a accesskey="p" href="math_toolkit/norms.html"><img src="../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="index.html"><img src="../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="index.html"><img src="../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="math_toolkit/number_series.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a>
    24. 

  24. </div>
    25. 

  25. <div class="chapter">
    26. 

  26. <div class="titlepage"><div><div><h1 class="title">
    27. 

  27. <a name="special"></a>Chapter&#160;8.&#160;Special Functions</h1></div></div></div>
    28. 

  28. <div class="toc">
    29. 

  29. <p><b>Table of Contents</b></p>
    30. 

  30. <dl class="toc">
    31. 

  31. <dt><span class="section"><a href="math_toolkit/number_series.html">Number Series</a></span></dt>
    32. 

  32. <dd><dl>
    33. 

  33. <dt><span class="section"><a href="math_toolkit/number_series/bernoulli_numbers.html">Bernoulli
    34. 

  34.       Numbers</a></span></dt>
    35. 

  35. <dt><span class="section"><a href="math_toolkit/number_series/tangent_numbers.html">Tangent Numbers</a></span></dt>
    36. 

  36. <dt><span class="section"><a href="math_toolkit/number_series/primes.html">Prime Numbers</a></span></dt>
    37. 

  37. </dl></dd>
    38. 

  38. <dt><span class="section"><a href="math_toolkit/sf_gamma.html">Gamma Functions</a></span></dt>
    39. 

  39. <dd><dl>
    40. 

  40. <dt><span class="section"><a href="math_toolkit/sf_gamma/tgamma.html">Gamma</a></span></dt>
    41. 

  41. <dt><span class="section"><a href="math_toolkit/sf_gamma/lgamma.html">Log Gamma</a></span></dt>
    42. 

  42. <dt><span class="section"><a href="math_toolkit/sf_gamma/digamma.html">Digamma</a></span></dt>
    43. 

  43. <dt><span class="section"><a href="math_toolkit/sf_gamma/trigamma.html">Trigamma</a></span></dt>
    44. 

  44. <dt><span class="section"><a href="math_toolkit/sf_gamma/polygamma.html">Polygamma</a></span></dt>
    45. 

  45. <dt><span class="section"><a href="math_toolkit/sf_gamma/gamma_ratios.html">Ratios of Gamma Functions</a></span></dt>
    46. 

  46. <dt><span class="section"><a href="math_toolkit/sf_gamma/igamma.html">Incomplete Gamma Functions</a></span></dt>
    47. 

  47. <dt><span class="section"><a href="math_toolkit/sf_gamma/igamma_inv.html">Incomplete Gamma Function
    48. 

  48.       Inverses</a></span></dt>
    49. 

  49. <dt><span class="section"><a href="math_toolkit/sf_gamma/gamma_derivatives.html">Derivative of
    50. 

  50.       the Incomplete Gamma Function</a></span></dt>
    51. 

  51. </dl></dd>
    52. 

  52. <dt><span class="section"><a href="math_toolkit/factorials.html">Factorials and Binomial Coefficients</a></span></dt>
    53. 

  53. <dd><dl>
    54. 

  54. <dt><span class="section"><a href="math_toolkit/factorials/sf_factorial.html">Factorial</a></span></dt>
    55. 

  55. <dt><span class="section"><a href="math_toolkit/factorials/sf_double_factorial.html">Double Factorial</a></span></dt>
    56. 

  56. <dt><span class="section"><a href="math_toolkit/factorials/sf_rising_factorial.html">Rising Factorial</a></span></dt>
    57. 

  57. <dt><span class="section"><a href="math_toolkit/factorials/sf_falling_factorial.html">Falling
    58. 

  58.       Factorial</a></span></dt>
    59. 

  59. <dt><span class="section"><a href="math_toolkit/factorials/sf_binomial.html">Binomial Coefficients</a></span></dt>
    60. 

  60. </dl></dd>
    61. 

  61. <dt><span class="section"><a href="math_toolkit/sf_beta.html">Beta Functions</a></span></dt>
    62. 

  62. <dd><dl>
    63. 

  63. <dt><span class="section"><a href="math_toolkit/sf_beta/beta_function.html">Beta</a></span></dt>
    64. 

  64. <dt><span class="section"><a href="math_toolkit/sf_beta/ibeta_function.html">Incomplete Beta
    65. 

  65.       Functions</a></span></dt>
    66. 

  66. <dt><span class="section"><a href="math_toolkit/sf_beta/ibeta_inv_function.html">The Incomplete
    67. 

  67.       Beta Function Inverses</a></span></dt>
    68. 

  68. <dt><span class="section"><a href="math_toolkit/sf_beta/beta_derivative.html">Derivative of the
    69. 

  69.       Incomplete Beta Function</a></span></dt>
    70. 

  70. </dl></dd>
    71. 

  71. <dt><span class="section"><a href="math_toolkit/sf_erf.html">Error Functions</a></span></dt>
    72. 

  72. <dd><dl>
    73. 

  73. <dt><span class="section"><a href="math_toolkit/sf_erf/error_function.html">Error Function erf
    74. 

  74.       and complement erfc</a></span></dt>
    75. 

  75. <dt><span class="section"><a href="math_toolkit/sf_erf/error_inv.html">Error Function Inverses</a></span></dt>
    76. 

  76. </dl></dd>
    77. 

  77. <dt><span class="section"><a href="math_toolkit/sf_poly.html">Polynomials</a></span></dt>
    78. 

  78. <dd><dl>
    79. 

  79. <dt><span class="section"><a href="math_toolkit/sf_poly/legendre.html">Legendre (and Associated)
    80. 

  80.       Polynomials</a></span></dt>
    81. 

  81. <dt><span class="section"><a href="math_toolkit/sf_poly/legendre_stieltjes.html">Legendre-Stieltjes
    82. 

  82.       Polynomials</a></span></dt>
    83. 

  83. <dt><span class="section"><a href="math_toolkit/sf_poly/laguerre.html">Laguerre (and Associated)
    84. 

  84.       Polynomials</a></span></dt>
    85. 

  85. <dt><span class="section"><a href="math_toolkit/sf_poly/hermite.html">Hermite Polynomials</a></span></dt>
    86. 

  86. <dt><span class="section"><a href="math_toolkit/sf_poly/chebyshev.html">Chebyshev Polynomials</a></span></dt>
    87. 

  87. <dt><span class="section"><a href="math_toolkit/sf_poly/sph_harm.html">Spherical Harmonics</a></span></dt>
    88. 

  88. <dt><span class="section"><a href="math_toolkit/sf_poly/cardinal_b_splines.html">Cardinal B-splines</a></span></dt>
    89. 

  89. <dt><span class="section"><a href="math_toolkit/sf_poly/gegenbauer.html">Gegenbauer Polynomials</a></span></dt>
    90. 

  90. <dt><span class="section"><a href="math_toolkit/sf_poly/jacobi.html">Jacobi Polynomials</a></span></dt>
    91. 

  91. </dl></dd>
    92. 

  92. <dt><span class="section"><a href="math_toolkit/bessel.html">Bessel Functions</a></span></dt>
    93. 

  93. <dd><dl>
    94. 

  94. <dt><span class="section"><a href="math_toolkit/bessel/bessel_over.html">Bessel Function Overview</a></span></dt>
    95. 

  95. <dt><span class="section"><a href="math_toolkit/bessel/bessel_first.html">Bessel Functions of
    96. 

  96.       the First and Second Kinds</a></span></dt>
    97. 

  97. <dt><span class="section"><a href="math_toolkit/bessel/bessel_root.html">Finding Zeros of Bessel
    98. 

  98.       Functions of the First and Second Kinds</a></span></dt>
    99. 

  99. <dt><span class="section"><a href="math_toolkit/bessel/mbessel.html">Modified Bessel Functions
    100. 

  100.       of the First and Second Kinds</a></span></dt>
    101. 

  101. <dt><span class="section"><a href="math_toolkit/bessel/sph_bessel.html">Spherical Bessel Functions
    102. 

  102.       of the First and Second Kinds</a></span></dt>
    103. 

  103. <dt><span class="section"><a href="math_toolkit/bessel/bessel_derivatives.html">Derivatives of
    104. 

  104.       the Bessel Functions</a></span></dt>
    105. 

  105. </dl></dd>
    106. 

  106. <dt><span class="section"><a href="math_toolkit/hankel.html">Hankel Functions</a></span></dt>
    107. 

  107. <dd><dl>
    108. 

  108. <dt><span class="section"><a href="math_toolkit/hankel/cyl_hankel.html">Cyclic Hankel Functions</a></span></dt>
    109. 

  109. <dt><span class="section"><a href="math_toolkit/hankel/sph_hankel.html">Spherical Hankel Functions</a></span></dt>
    110. 

  110. </dl></dd>
    111. 

  111. <dt><span class="section"><a href="math_toolkit/airy.html">Airy Functions</a></span></dt>
    112. 

  112. <dd><dl>
    113. 

  113. <dt><span class="section"><a href="math_toolkit/airy/ai.html">Airy Ai Function</a></span></dt>
    114. 

  114. <dt><span class="section"><a href="math_toolkit/airy/bi.html">Airy Bi Function</a></span></dt>
    115. 

  115. <dt><span class="section"><a href="math_toolkit/airy/aip.html">Airy Ai' Function</a></span></dt>
    116. 

  116. <dt><span class="section"><a href="math_toolkit/airy/bip.html">Airy Bi' Function</a></span></dt>
    117. 

  117. <dt><span class="section"><a href="math_toolkit/airy/airy_root.html">Finding Zeros of Airy Functions</a></span></dt>
    118. 

  118. </dl></dd>
    119. 

  119. <dt><span class="section"><a href="math_toolkit/ellint.html">Elliptic Integrals</a></span></dt>
    120. 

  120. <dd><dl>
    121. 

  121. <dt><span class="section"><a href="math_toolkit/ellint/ellint_intro.html">Elliptic Integral Overview</a></span></dt>
    122. 

  122. <dt><span class="section"><a href="math_toolkit/ellint/ellint_carlson.html">Elliptic Integrals
    123. 

  123.       - Carlson Form</a></span></dt>
    124. 

  124. <dt><span class="section"><a href="math_toolkit/ellint/ellint_1.html">Elliptic Integrals of the
    125. 

  125.       First Kind - Legendre Form</a></span></dt>
    126. 

  126. <dt><span class="section"><a href="math_toolkit/ellint/ellint_2.html">Elliptic Integrals of the
    127. 

  127.       Second Kind - Legendre Form</a></span></dt>
    128. 

  128. <dt><span class="section"><a href="math_toolkit/ellint/ellint_3.html">Elliptic Integrals of the
    129. 

  129.       Third Kind - Legendre Form</a></span></dt>
    130. 

  130. <dt><span class="section"><a href="math_toolkit/ellint/ellint_d.html">Elliptic Integral D - Legendre
    131. 

  131.       Form</a></span></dt>
    132. 

  132. <dt><span class="section"><a href="math_toolkit/ellint/jacobi_zeta.html">Jacobi Zeta Function</a></span></dt>
    133. 

  133. <dt><span class="section"><a href="math_toolkit/ellint/heuman_lambda.html">Heuman Lambda Function</a></span></dt>
    134. 

  134. </dl></dd>
    135. 

  135. <dt><span class="section"><a href="math_toolkit/jacobi.html">Jacobi Elliptic Functions</a></span></dt>
    136. 

  136. <dd><dl>
    137. 

  137. <dt><span class="section"><a href="math_toolkit/jacobi/jac_over.html">Overview of the Jacobi
    138. 

  138.       Elliptic Functions</a></span></dt>
    139. 

  139. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_elliptic.html">Jacobi Elliptic
    140. 

  140.       SN, CN and DN</a></span></dt>
    141. 

  141. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cd.html">Jacobi Elliptic Function
    142. 

  142.       cd</a></span></dt>
    143. 

  143. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cn.html">Jacobi Elliptic Function
    144. 

  144.       cn</a></span></dt>
    145. 

  145. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cs.html">Jacobi Elliptic Function
    146. 

  146.       cs</a></span></dt>
    147. 

  147. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_dc.html">Jacobi Elliptic Function
    148. 

  148.       dc</a></span></dt>
    149. 

  149. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_dn.html">Jacobi Elliptic Function
    150. 

  150.       dn</a></span></dt>
    151. 

  151. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_ds.html">Jacobi Elliptic Function
    152. 

  152.       ds</a></span></dt>
    153. 

  153. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_nc.html">Jacobi Elliptic Function
    154. 

  154.       nc</a></span></dt>
    155. 

  155. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_nd.html">Jacobi Elliptic Function
    156. 

  156.       nd</a></span></dt>
    157. 

  157. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_ns.html">Jacobi Elliptic Function
    158. 

  158.       ns</a></span></dt>
    159. 

  159. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sc.html">Jacobi Elliptic Function
    160. 

  160.       sc</a></span></dt>
    161. 

  161. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sd.html">Jacobi Elliptic Function
    162. 

  162.       sd</a></span></dt>
    163. 

  163. <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sn.html">Jacobi Elliptic Function
    164. 

  164.       sn</a></span></dt>
    165. 

  165. </dl></dd>
    166. 

  166. <dt><span class="section"><a href="math_toolkit/lambert_w.html">Lambert <span class="emphasis"><em>W</em></span>
    167. 

  167.     function</a></span></dt>
    168. 

  168. <dt><span class="section"><a href="math_toolkit/zetas.html">Zeta Functions</a></span></dt>
    169. 

  169. <dd><dl><dt><span class="section"><a href="math_toolkit/zetas/zeta.html">Riemann Zeta Function</a></span></dt></dl></dd>
    170. 

  170. <dt><span class="section"><a href="math_toolkit/expint.html">Exponential Integrals</a></span></dt>
    171. 

  171. <dd><dl>
    172. 

  172. <dt><span class="section"><a href="math_toolkit/expint/expint_n.html">Exponential Integral En</a></span></dt>
    173. 

  173. <dt><span class="section"><a href="math_toolkit/expint/expint_i.html">Exponential Integral Ei</a></span></dt>
    174. 

  174. </dl></dd>
    175. 

  175. <dt><span class="section"><a href="math_toolkit/hypergeometric.html">Hypergeometric Functions</a></span></dt>
    176. 

  176. <dd><dl>
    177. 

  177. <dt><span class="section"><a href="math_toolkit/hypergeometric/hypergeometric_1f0.html">Hypergeometric
    178. 

  178.       <sub>1</sub><span class="emphasis"><em>F</em></span><sub>0</sub> </a></span></dt>
    179. 

  179. <dt><span class="section"><a href="math_toolkit/hypergeometric/hypergeometric_0f1.html">Hypergeometric
    180. 

  180.       <sub>0</sub><span class="emphasis"><em>F</em></span><sub>1</sub> </a></span></dt>
    181. 

  181. <dt><span class="section"><a href="math_toolkit/hypergeometric/hypergeometric_2f0.html">Hypergeometric
    182. 

  182.       <sub>2</sub><span class="emphasis"><em>F</em></span><sub>0</sub></a></span></dt>
    183. 

  183. <dt><span class="section"><a href="math_toolkit/hypergeometric/hypergeometric_1f1.html">Hypergeometric
    184. 

  184.       <sub>1</sub><span class="emphasis"><em>F</em></span><sub>1</sub></a></span></dt>
    185. 

  185. <dt><span class="section"><a href="math_toolkit/hypergeometric/hypergeometric_pfq.html">Hypergeometric
    186. 

  186.       <sub>p</sub>F<sub>q</sub></a></span></dt>
    187. 

  187. <dt><span class="section"><a href="math_toolkit/hypergeometric/hypergeometric_refs.html">Hypergeometric
    188. 

  188.       References</a></span></dt>
    189. 

  189. </dl></dd>
    190. 

  190. <dt><span class="section"><a href="math_toolkit/powers.html">Basic Functions</a></span></dt>
    191. 

  191. <dd><dl>
    192. 

  192. <dt><span class="section"><a href="math_toolkit/powers/sin_pi.html">sin_pi</a></span></dt>
    193. 

  193. <dt><span class="section"><a href="math_toolkit/powers/cos_pi.html">cos_pi</a></span></dt>
    194. 

  194. <dt><span class="section"><a href="math_toolkit/powers/log1p.html">log1p</a></span></dt>
    195. 

  195. <dt><span class="section"><a href="math_toolkit/powers/expm1.html">expm1</a></span></dt>
    196. 

  196. <dt><span class="section"><a href="math_toolkit/powers/cbrt.html">cbrt</a></span></dt>
    197. 

  197. <dt><span class="section"><a href="math_toolkit/powers/sqrt1pm1.html">sqrt1pm1</a></span></dt>
    198. 

  198. <dt><span class="section"><a href="math_toolkit/powers/powm1.html">powm1</a></span></dt>
    199. 

  199. <dt><span class="section"><a href="math_toolkit/powers/hypot.html">hypot</a></span></dt>
    200. 

  200. <dt><span class="section"><a href="math_toolkit/powers/ct_pow.html">Compile Time Power of a Runtime
    201. 

  201.       Base</a></span></dt>
    202. 

  202. </dl></dd>
    203. 

  203. <dt><span class="section"><a href="math_toolkit/sinc.html">Sinus Cardinal and Hyperbolic Sinus
    204. 

  204.     Cardinal Functions</a></span></dt>
    205. 

  205. <dd><dl>
    206. 

  206. <dt><span class="section"><a href="math_toolkit/sinc/sinc_overview.html">Sinus Cardinal and Hyperbolic
    207. 

  207.       Sinus Cardinal Functions Overview</a></span></dt>
    208. 

  208. <dt><span class="section"><a href="math_toolkit/sinc/sinc_pi.html">sinc_pi</a></span></dt>
    209. 

  209. <dt><span class="section"><a href="math_toolkit/sinc/sinhc_pi.html">sinhc_pi</a></span></dt>
    210. 

  210. </dl></dd>
    211. 

  211. <dt><span class="section"><a href="math_toolkit/inv_hyper.html">Inverse Hyperbolic Functions</a></span></dt>
    212. 

  212. <dd><dl>
    213. 

  213. <dt><span class="section"><a href="math_toolkit/inv_hyper/inv_hyper_over.html">Inverse Hyperbolic
    214. 

  214.       Functions Overview</a></span></dt>
    215. 

  215. <dt><span class="section"><a href="math_toolkit/inv_hyper/acosh.html">acosh</a></span></dt>
    216. 

  216. <dt><span class="section"><a href="math_toolkit/inv_hyper/asinh.html">asinh</a></span></dt>
    217. 

  217. <dt><span class="section"><a href="math_toolkit/inv_hyper/atanh.html">atanh</a></span></dt>
    218. 

  218. </dl></dd>
    219. 

  219. <dt><span class="section"><a href="math_toolkit/owens_t.html">Owen's T function</a></span></dt>
    220. 

  220. </dl>
    221. 

  221. </div>
    222. 

  222. </div>
    223. 

  223. <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
    224. 

  224. <td align="left"></td>
    225. 

  225. <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
    226. 

  226.       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
    227. 

  227.       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
    228. 

  228.       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
    229. 

  229.       Daryle Walker and Xiaogang Zhang<p>
    230. 

  230.         Distributed under the Boost Software License, Version 1.0. (See accompanying
    231. 

  231.         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
    232. 

  232.       </p>
    233. 

  233. </div></td>
    234. 

  234. </tr></table>
    235. 

  235. <hr>
    236. 

  236. <div class="spirit-nav">
    237. 

  237. <a accesskey="p" href="math_toolkit/norms.html"><img src="../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="index.html"><img src="../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="index.html"><img src="../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="math_toolkit/number_series.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a>
    238. 

  238. </div>
    239. 

  239. </body>
    240. 

  240. </html>
    241.