Created by Stephen L. Moshier, Giuseppe Borzi (gborzi@dees.unict.it), Viacheslav N. Mezentsev (viacheslavmezentsev@ya.ru) in the scope of SMath project. Published by Вячеслав Мезенцев.
This is Open Source project. Sources shared under MIT Licence and available in public SVN repository.

Features of Cephes Mathematical Library

Version 1.0.8034.38340

Functions

Additional components that add new mathematical functions to the SMath Studio program, necessary for solving problems from various fields.

  1. Ae("complexNumber")
    (x) Exponentially scaled first Airy function of complex argument.
  2. Aep("complexNumber")
    (x) Exponentially scaled derivative of first Airy function of complex argument.
  3. Ai("complexNumber")
    (x) First Airy function, solution of the differential equation y"=xy. The argument can be complex
  4. Aip("complexNumber")
    (x) Derivative of the first Airy function, solution of the differential equation y"=xy. The argument can be complex
  5. Be("complexNumber")
    (x) Exponentially scaled second Airy function of complex argument.
  6. Bep("complexNumber")
    (x) Exponentially scaled first derivative of second Airy function of complex argument.
  7. beta("1:complexNumber", "2:complexNumber")
    (x,y) Beta function or Euler's integral of the first kind. The arguments can be complex
  8. Bi("complexNumber")
    (x) Second Airy function, solution of the differential equation y"=xy. The argument can be complex
  9. binomial("1:complexNumber", "2:complexNumber")
    (a,k) Binomial coefficient, a is real k must be a non negative integer.
  10. Bip("complexNumber")
    (x) Derivative of the second Airy function, solution of the differential equation y"=xy. The argument can be complex
  11. Chi("complexNumber")
    (x) Hyperbolic cosine integral of real argument.
  12. Ci("complexNumber")
    (x) Cosine integral of real argument.
  13. cn("1:complexNumber", "2:complexNumber")
    (u,k) Jacobian elliptic functions cn(u,k) of real arguments.
  14. csgn("complexNumber")
    (x) Complex sign of x.
  15. Dawson("complexNumber")
    (x) Dawson's Integral of real argument.
  16. dilog("complexNumber")
    (x) Dilogarithm function of real argument.
  17. dn("1:complexNumber", "2:complexNumber")
    (u,k) Jacobian elliptic functions dn(u,k) of real arguments.
  18. Ei("1:complexNumber", "2:complexNumber")
    (n,x) Exponential integral Ei. n in an integer, x is real.
  19. FresnelC("complexNumber")
    (x) Fresnel integral C(x) of real argument.
  20. FresnelS("complexNumber")
    (x) Fresnel integral S(x) of real argument.
  21. H1e("1:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber", "3:complexNumber")
    (a,b,x) Confluent hypergeometric function 1F1 with real arguments.
  28. hyp1f2("1:complexNumber", "2:complexNumber", "3:complexNumber", "4:complexNumber")
    (a,b,c,x) Hypergeometric function 1F2 with real arguments.
  29. hyp2f0("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (a,b,x) Hypergeometric function 2F0 with real arguments.
  30. hyp2f1("1:complexNumber", "2:complexNumber", "3:complexNumber", "4:complexNumber")
    (a,b,c,x) Gauss hypergeometric function 2F1 with real arguments.
  31. hyp3f0("1:complexNumber", "2:complexNumber", "3:complexNumber", "4:complexNumber")
    (a,b,c,x) Hypergeometric function 3F0 with real arguments.
  32. ibeta("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (a,b,x) Incomplete beta integral; the domain of definition is 0<=x<=1, a>0 and b>0.
  33. ibetai("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (a,b,x) Inverse of incomplete beta integral; the domain of definition is a>0 and b>0.
  34. Ie("1:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (a,x) Incomplete gamma integral; both arguments must be real and positive.
  36. igamc("1:complexNumber", "2:complexNumber")
    (a,x) Complemented incomplete gamma integral; both arguments must be real and positive.
  37. igami("1:complexNumber", "2:complexNumber")
    (a,x) Inverse of complemented imcomplete gamma integral of real arguments.
  38. Iv("1:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (x,y) Natural logarithm of beta function. Arguments are considered in the cut plane -pi < arg(z) <= pi.
  45. LegendreE("1:complexNumber", "2:complexNumber")
    (x,k) Legendre's canonical incomplete elliptic integral of the second kind with real arguments.
  46. LegendreEc("complexNumber")
    (k) Legendre's complete elliptic integral of the second kind with real argument.
  47. LegendreEc1("complexNumber")
    (k) Associated Legendre's complete elliptic integral of the second kind with real argument.
  48. LegendreF("1:complexNumber", "2:complexNumber")
    (x,k) Legendre's canonical incomplete elliptic integral of the first kind with real arguments.
  49. LegendreKc("complexNumber")
    (k) Legendre's complete elliptic integral of the first kind with real argument.
  50. LegendreKc1("complexNumber")
    (k) Associated Legendre's complete elliptic integral of the first kind with real argument.
  51. LegendreP("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (x,n,k) Legendre's canonical incomplete elliptic integral of the third kind with real arguments.
  52. LegendrePc("1:complexNumber", "2:complexNumber")
    (n,k) Legendre's complete elliptic integral of the third kind with real arguments.
  53. LegendrePc1("1:complexNumber", "2:complexNumber")
    (n,k) Associated Legendre's complete elliptic integral of the third kind with real arguments.
  54. lgam("complexNumber")
    (z) Natural logarithm of gamma function. Argument z is considered in the cut plane -pi < arg(z) <= pi.
  55. mask("complexNumber")
    (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:complexNumber", "2:complexNumber")
    (u,k) Amplitude of jacobian elliptic functions phi(u,k) of real arguments.
  57. plm("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (l,m,x) Normalized first kind Legendre polynomials and associated functions of integer degree l and integer order m.
  58. Plm("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (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("complexNumber")
    (z) Logarithmic derivative of the gamma function. The argument can be complex
  60. Qlm("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (l,m,x) Second kind Legendre functions of degree l, integer order m and argument 0<=x<1.
  61. Rd("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (x,y,z) Carlson's incomplete elliptic integral of the second kind with real argument.
  62. Rf("1:complexNumber", "2:complexNumber", "3:complexNumber")
    (x,y,z) Carlson's incomplete elliptic integral of the first kind with real arguments.
  63. rgam("complexNumber")
    (x) Returns one divided by the gamma function of the argument.
  64. Rj("1:complexNumber", "2:complexNumber", "3:complexNumber", "4:complexNumber")
    (x,y,z,p) Carlson's incomplete elliptic integral of the third kind with real argument.
  65. round("complexNumber")
    (x) Round real x to nearest or even integer number.
  66. sfact("complexNumber")
    (n) Semifactorial of integer n.
  67. Shi("complexNumber")
    (x) Hyperbolic sine integral of real argument.
  68. Si("complexNumber")
    (x) Sine integral of real argument.
  69. signum("complexNumber")
    (x) Sign of x.
  70. sn("1:complexNumber", "2:complexNumber")
    (u,k) Jacobian elliptic functions sn(u,k) of real arguments.
  71. Struve("1:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber", "3:complexNumber")
    (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:complexNumber", "2:complexNumber", "3:complexNumber", "4:complexNumber")
    (l,m,theta,phi) Spherical harmonic of integer degree l, integer order m, latitude theta in [-PI,PI] and longitude phi.
  75. yv("1:complexNumber", "2:complexNumber")
    (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:complexNumber", "2:complexNumber")
    (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("complexNumber")
    (x) Riemann zeta function of real argument. x must be positive
  78. Zeta2("1:complexNumber", "2:complexNumber")
    (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.