JLFloatSpecialFunctions2

jfsf2.spad line 1 [edit on github]

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

airyAi: JLFloat -> JLFloat

airyAi(z) computes Airy Ai function at z

besselJ0: JLFloat -> JLFloat

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

besselJ1: JLFloat -> JLFloat

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

besselY0: JLFloat -> JLFloat

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

besselY1: JLFloat -> JLFloat

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

Beta: (JLFloat, JLFloat) -> JLFloat

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

digamma: JLFloat -> JLFloat

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

Ei: JLFloat -> JLFloat

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

erf: (JLFloat, JLFloat) -> JLFloat

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

erf: JLFloat -> JLFloat

erf(x) computes error function at x.

erfc: JLFloat -> JLFloat

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

erfcx: JLFloat -> JLFloat

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

eta: JLFloat -> JLFloat

eta(x) computes Dirichlet eta function at x.

expint: (JLFloat, JLFloat) -> JLFloat

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

Gamma: (JLFloat, JLFloat) -> JLFloat

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

Gamma: JLFloat -> JLFloat

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

inverseErf: JLFloat -> JLFloat

inverseErf(x) computes inverse function of erf.

inverseErfc: JLFloat -> JLFloat

inverseErfc(x) computes the inverse function of erfc.

jinc: JLFloat -> JLFloat

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

logBeta: (JLFloat, JLFloat) -> JLFloat

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

logerfc: JLFloat -> JLFloat

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

logerfcx: JLFloat -> JLFloat

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

logGamma: (JLFloat, JLFloat) -> JLFloat

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

logGamma: JLFloat -> JLFloat

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

riemannZeta: JLFloat -> JLFloat

riemannZeta(x) computes Riemann zeta function at x.