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constituents

  • modf, fmod (inv of modf)

  • floor, ceil, trunc

  • round

  • rem, mod

  • div, cld, fld

  • divrem, fldmod

arithmetic functions

  • +,-, *, /
  • square, cube, sqrt, cbrt, hypot
  • pow(x,i), root(x,i) where i is an integer > 0
  • factorial, doublefactorial, risingfactorial
  • binomial

complex constituents

  • real, imag
  • angle, magnitude
  • conj # applies to a value and applies to a matrix

random numbers

  • rand, randn

arithmetic-geometric mean

  • agm, agm1

All of the following functions are available for ArbFloat, ArbReal and ArbComplex types

elementary functions

  • exp, expm1
  • log, log1p, log2, log10
  • sin, cos, tan, csc, sec, cot
  • sinpi, cospi, tanpi, cotpi
  • asin, acos, atan, atan(y,x)
  • sinh, cosh, tanh, csch, sech, coth
  • asinh, acosh, atanh

gamma functions

  • gamma, lgamma
  • rgamma, digamma

error functions

  • erf, erfc, erfi

Bessel functions

  • besselj, besselj0, besselj1
  • bessely, bessely0, bessely1
  • besseli, besselk

Airy functions

  • airyai, airyaiprime
  • airybi, airybiprime

elliptic functions

  • elliptic_e, elliptic_k, elliptic_pi (complete and incomplete integrals)
  • elliptic_e2, elliptic_k2, elliptic_pi2 (squares the modulus)
  • elliptic_rf, elliptic_rg, elliptic_rj (Carleson's symmetric integrals)

other special functions

  • ei, si, ci
  • shi, chi
  • zeta, eta, xi # Reimann
  • polylog, lambertw

transforms

  • dft, inverse_dft