JuliaFloatSpecialFunctions2

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Special functions computed using Julia's ecosystem. They are here essentially for “completeness” purpose with JuliaFloat.

airyAi: JuliaFloat -> JuliaFloat

airyAi(z) computes Airy Ai function at z

besselJ0: JuliaFloat -> JuliaFloat

besselJ0(z) computes besselj(0,z).

besselJ1: JuliaFloat -> JuliaFloat

besselJ1(z) computes besselj(1,z).

besselY0: JuliaFloat -> JuliaFloat

besselY0(z) computes bessely(0,z).

besselY1: JuliaFloat -> JuliaFloat

besselY1(z) computes bessely(1,z).

Beta: (JuliaFloat, JuliaFloat) -> JuliaFloat

Beta(x,y) computes beta function at x,y.

digamma: JuliaFloat -> JuliaFloat

digamma(x) computes digamma function (i.e. the derivative of logGamma at x).

Ei: JuliaFloat -> JuliaFloat

Ei(x) computes exponential integral Ei(x).

erf: (JuliaFloat, JuliaFloat) -> JuliaFloat

erf(x,y) computes accurate version of erf(y) - erf(x).

erf: JuliaFloat -> JuliaFloat

erf(x) computes error function at x.

erfc: JuliaFloat -> JuliaFloat

erfc(x) computes complementary error function, i.e. the accurate version of 1-erf(x) for large x.

erfcx: JuliaFloat -> JuliaFloat

erfcx(x) computes scaled complementary error function, i.e. accurate e^{x^2} erfc(x) for large x.

eta: JuliaFloat -> JuliaFloat

eta(x) computes Dirichlet eta function at x.

expint: (JuliaFloat, JuliaFloat) -> JuliaFloat

expint(nu, z) computes exponential integral Enu(z).

Gamma: (JuliaFloat, JuliaFloat) -> JuliaFloat

Gamma(a,z) computes upper incomplete gamma function Gamma(a,z).

Gamma: JuliaFloat -> JuliaFloat

Gamma(z) computes gamma function Gamma(z).

inverseErf: JuliaFloat -> JuliaFloat

inverseErf(x) computes inverse function of erf.

inverseErfc: JuliaFloat -> JuliaFloat

inverseErfc(x) computes the inverse function of erfc.

jinc: JuliaFloat -> JuliaFloat

jinc(x) computes scaled Bessel function of the first kind divided by x. A.k.a. sombrero or besinc.

logBeta: (JuliaFloat, JuliaFloat) -> JuliaFloat

logBeta(x,y) computes accurate log(beta(x,y)) for large x or y.

logerfc: JuliaFloat -> JuliaFloat

logerfc(x) computes log of the complementary error function, i.e. accurate ln(erfc(x)) for large x.

logerfcx: JuliaFloat -> JuliaFloat

logerfcx(x) computes log of the scaled complementary error function, i.e. accurate ln(erfcx(x)) for large negative x.

logGamma: (JuliaFloat, JuliaFloat) -> JuliaFloat

logGamma(a,z) computes accurate log(gamma(a,x)) for large arguments.

logGamma: JuliaFloat -> JuliaFloat

logGamma(x) computes accurate log(gamma(x)) for large x.

riemannZeta: JuliaFloat -> JuliaFloat

riemannZeta(x) computes Riemann zeta function at x.