Автор: Stephen L. Moshier, Giuseppe Borzi (gborzi@dees.unict.it), Viacheslav N. Mezentsev (viacheslavmezentsev@ya.ru). Создано в рамках проекта SMath. Опубликовано пользователем Вячеслав Мезенцев.
Это проект с открытыми исходными кодами. Исходные коды опубликованы под лицензией MIT и доступны в публичном хранилище SVN.

Функциональность Cephes Mathematical Library

Версия 1.0.8034.38340

Функции

Дополнительные компоненты, добавляющие в программу SMath Studio новые математические функции, необходимые для решения задач из различных областей.

  1. Ae("комплексноеЧисло")
    (x) Exponentially scaled first Airy function of complex argument.
  2. Aep("комплексноеЧисло")
    (x) Exponentially scaled derivative of first Airy function of complex argument.
  3. Ai("комплексноеЧисло")
    (x) First Airy function, solution of the differential equation y"=xy. The argument can be complex
  4. Aip("комплексноеЧисло")
    (x) Derivative of the first Airy function, solution of the differential equation y"=xy. The argument can be complex
  5. Be("комплексноеЧисло")
    (x) Exponentially scaled second Airy function of complex argument.
  6. Bep("комплексноеЧисло")
    (x) Exponentially scaled first derivative of second Airy function of complex argument.
  7. beta("1:комплексноеЧисло", "2:комплексноеЧисло")
    (x,y) Beta function or Euler's integral of the first kind. The arguments can be complex
  8. Bi("комплексноеЧисло")
    (x) Second Airy function, solution of the differential equation y"=xy. The argument can be complex
  9. binomial("1:комплексноеЧисло", "2:комплексноеЧисло")
    (a,k) Binomial coefficient, a is real k must be a non negative integer.
  10. Bip("комплексноеЧисло")
    (x) Derivative of the second Airy function, solution of the differential equation y"=xy. The argument can be complex
  11. Chi("комплексноеЧисло")
    (x) Hyperbolic cosine integral of real argument.
  12. Ci("комплексноеЧисло")
    (x) Cosine integral of real argument.
  13. cn("1:комплексноеЧисло", "2:комплексноеЧисло")
    (u,k) Jacobian elliptic functions cn(u,k) of real arguments.
  14. csgn("комплексноеЧисло")
    (x) Complex sign of x.
  15. Dawson("комплексноеЧисло")
    (x) Dawson's Integral of real argument.
  16. dilog("комплексноеЧисло")
    (x) Dilogarithm function of real argument.
  17. dn("1:комплексноеЧисло", "2:комплексноеЧисло")
    (u,k) Jacobian elliptic functions dn(u,k) of real arguments.
  18. Ei("1:комплексноеЧисло", "2:комплексноеЧисло")
    (n,x) Exponential integral Ei. n in an integer, x is real.
  19. FresnelC("комплексноеЧисло")
    (x) Fresnel integral C(x) of real argument.
  20. FresnelS("комплексноеЧисло")
    (x) Fresnel integral S(x) of real argument.
  21. H1e("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Exponentially scaled Hankel function of real order v and complex argument z (1st kind). Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  22. h1v("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,x) Spherical Hankel function of real order v and complex argument z (1st kind). Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  23. H1v("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Hankel function of real order v and complex argument z (1st kind). Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  24. H2e("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Exponentially scaled Hankel function of real order v and complex argument z (2nd kind). Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  25. h2v("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,x) Spherical Hankel function of real order v and complex argument z (2nd kind). Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  26. H2v("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Hankel function of real order v and complex argument z (2nd kind). Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  27. hyp1f1("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (a,b,x) Confluent hypergeometric function 1F1 with real arguments.
  28. hyp1f2("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло", "4:комплексноеЧисло")
    (a,b,c,x) Hypergeometric function 1F2 with real arguments.
  29. hyp2f0("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (a,b,x) Hypergeometric function 2F0 with real arguments.
  30. hyp2f1("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло", "4:комплексноеЧисло")
    (a,b,c,x) Gauss hypergeometric function 2F1 with real arguments.
  31. hyp3f0("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло", "4:комплексноеЧисло")
    (a,b,c,x) Hypergeometric function 3F0 with real arguments.
  32. ibeta("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (a,b,x) Incomplete beta integral; the domain of definition is 0<=x<=1, a>0 and b>0.
  33. ibetai("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (a,b,x) Inverse of incomplete beta integral; the domain of definition is a>0 and b>0.
  34. Ie("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Exponentially scaled modified Bessel function of real order v and complex argument z. Argument z is considered in the cut plane -pi < arg(z) <= pi.
  35. igam("1:комплексноеЧисло", "2:комплексноеЧисло")
    (a,x) Incomplete gamma integral; both arguments must be real and positive.
  36. igamc("1:комплексноеЧисло", "2:комплексноеЧисло")
    (a,x) Complemented incomplete gamma integral; both arguments must be real and positive.
  37. igami("1:комплексноеЧисло", "2:комплексноеЧисло")
    (a,x) Inverse of complemented imcomplete gamma integral of real arguments.
  38. Iv("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Modified Bessel function of real order v and complex argument z. Argument z is considered in the cut plane -pi < arg(z) <= pi.
  39. Je("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Exponentially scaled Bessel function of real order v and complex argument z. Argument z is considered in the cut plane -pi < arg(z) <= pi.
  40. jv("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,x) Spherical Bessel function of real order v and complex argument z. Argument z is considered in the cut plane -pi < arg(z) <= pi.
  41. Jv("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Bessel function of real order v and complex argument z. Argument z is considered in the cut plane -pi < arg(z) <= pi.
  42. Ke("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Exponentially scaled modified Bessel function of the third kind of real order v and complex argument z. Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  43. Kv("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Modified Bessel function of the third kind of real order v and complex argument z. Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  44. lbeta("1:комплексноеЧисло", "2:комплексноеЧисло")
    (x,y) Natural logarithm of beta function. Arguments are considered in the cut plane -pi < arg(z) <= pi.
  45. LegendreE("1:комплексноеЧисло", "2:комплексноеЧисло")
    (x,k) Legendre's canonical incomplete elliptic integral of the second kind with real arguments.
  46. LegendreEc("комплексноеЧисло")
    (k) Legendre's complete elliptic integral of the second kind with real argument.
  47. LegendreEc1("комплексноеЧисло")
    (k) Associated Legendre's complete elliptic integral of the second kind with real argument.
  48. LegendreF("1:комплексноеЧисло", "2:комплексноеЧисло")
    (x,k) Legendre's canonical incomplete elliptic integral of the first kind with real arguments.
  49. LegendreKc("комплексноеЧисло")
    (k) Legendre's complete elliptic integral of the first kind with real argument.
  50. LegendreKc1("комплексноеЧисло")
    (k) Associated Legendre's complete elliptic integral of the first kind with real argument.
  51. LegendreP("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (x,n,k) Legendre's canonical incomplete elliptic integral of the third kind with real arguments.
  52. LegendrePc("1:комплексноеЧисло", "2:комплексноеЧисло")
    (n,k) Legendre's complete elliptic integral of the third kind with real arguments.
  53. LegendrePc1("1:комплексноеЧисло", "2:комплексноеЧисло")
    (n,k) Associated Legendre's complete elliptic integral of the third kind with real arguments.
  54. lgam("комплексноеЧисло")
    (z) Natural logarithm of gamma function. Argument z is considered in the cut plane -pi < arg(z) <= pi.
  55. mask("комплексноеЧисло")
    (x) Masks and unmasks the partial loss of precision error. If called with x = 0 that error message is disabled, if called with x != 0 that error message is enabled. Returns the previous state; default is unmasked.
  56. phi("1:комплексноеЧисло", "2:комплексноеЧисло")
    (u,k) Amplitude of jacobian elliptic functions phi(u,k) of real arguments.
  57. plm("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (l,m,x) Normalized first kind Legendre polynomials and associated functions of integer degree l and integer order m.
  58. Plm("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (l,m,x) First kind Legendre polynomials and associated functions of degree l and integer order m. Plm(l,m,x) = (-1)^m (1-x^2)^(m/2) d^m( Pn(n,x) )/dx^m where l and x must be real and Pn(n,x) is the Legendre polynomial.
  59. Psi("комплексноеЧисло")
    (z) Logarithmic derivative of the gamma function. The argument can be complex
  60. Qlm("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (l,m,x) Second kind Legendre functions of degree l, integer order m and argument 0<=x<1.
  61. Rd("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (x,y,z) Carlson's incomplete elliptic integral of the second kind with real argument.
  62. Rf("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (x,y,z) Carlson's incomplete elliptic integral of the first kind with real arguments.
  63. rgam("комплексноеЧисло")
    (x) Returns one divided by the gamma function of the argument.
  64. Rj("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло", "4:комплексноеЧисло")
    (x,y,z,p) Carlson's incomplete elliptic integral of the third kind with real argument.
  65. round("комплексноеЧисло")
    (x) Round real x to nearest or even integer number.
  66. sfact("комплексноеЧисло")
    (n) Semifactorial of integer n.
  67. Shi("комплексноеЧисло")
    (x) Hyperbolic sine integral of real argument.
  68. Si("комплексноеЧисло")
    (x) Sine integral of real argument.
  69. signum("комплексноеЧисло")
    (x) Sign of x.
  70. sn("1:комплексноеЧисло", "2:комплексноеЧисло")
    (u,k) Jacobian elliptic functions sn(u,k) of real arguments.
  71. Struve("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,x) Computes the Struve function of real order v and real argument x. Negative x is rejected unless v is an integer.
  72. Ye("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Exponentially scaled Neumann function of real order v and complex argument z. Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  73. Yl("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло")
    (l,theta,phi) Sequence of spherical harmonic of integer degree l, integer order m=0..l, latitude theta in [-PI,PI] and longitude phi.
  74. Ylm("1:комплексноеЧисло", "2:комплексноеЧисло", "3:комплексноеЧисло", "4:комплексноеЧисло")
    (l,m,theta,phi) Spherical harmonic of integer degree l, integer order m, latitude theta in [-PI,PI] and longitude phi.
  75. yv("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,x) Spherical Neumann function of real order v and complex argument z. Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  76. Yv("1:комплексноеЧисло", "2:комплексноеЧисло")
    (v,z) Neumann function of real order v and complex argument z. Argument z must be nonzero and is considered in the cut plane -pi < arg(z) <= pi.
  77. Zeta("комплексноеЧисло")
    (x) Riemann zeta function of real argument. x must be positive
  78. Zeta2("1:комплексноеЧисло", "2:комплексноеЧисло")
    (x,q) Riemann zeta function of two arguments. It is the sum, for k integer ranging from 0 to infinity, of (k+q)^-x where q is a positive integer and x > 1.