Special Functions

DoubleFloats supports some special functions of real values.

x below is any of Double64, Double32, Double16

Bessel Functions

• besselj0(x), besselj1(x)`

  • besselj(0, x), besselj(1, x)

• bessely0(x), bessely1(x)

  • bessely(0, x), bessely(1, x)

• besselj(nu::Int, x)

  • Bessel function of the first kind

• bessely(nu::Int, x)

  • Bessel function of the second kind

Gamma Functions

• gamma(x)
  • gamma function
• loggamma(x), lgamma(x)
  • log gamma function

Error Functions

• erf(x)
  • error function
• erfc(x)
  • complementary error function (1-erf(x))

Arithmetic-Geometric Mean

• agm(a, b), agm1(x) = agm(1, x)
  • converges for all same-signed operands; the iteration stops at its roundoff floor, so no operand scale can stall it

Elliptic Integrals

• ellipk(m)
  • Complete Elliptic Integral of the First Kind, K(m) with parameter m
  • accurate over the whole domain 0 <= m < 1, including arbitrarily close to m = 1