JLFloat64SpecialFunctions2

jf64sf2.spad line 1 [edit on github]

Special functions computed using Julia's ecosystem. They are here essentially for “completeness” purpose with JLFloat64. You should use the DoubleFloat's special functions if available, calling Julia functions is costly.

airyAi: JLFloat64 -> JLFloat64

airyAi(z) computes Airy Ai function at z

airyAiPrime: JLFloat64 -> JLFloat64

airyAiPrime(z) computes derivative of the Airy Ai function at z

airyAiPrimex: JLFloat64 -> JLFloat64

airyAiPrimex(z) computes scaled derivative of the Airy Ai function at z

airyAix: JLFloat64 -> JLFloat64

airyAix(z) computes scaled Airy Ai function and kth derivatives at z

airyBi: JLFloat64 -> JLFloat64

airyBi(z) computes Airy Bi function at z

airyBiPrime: JLFloat64 -> JLFloat64

airyBiPrime(z) computes derivative of the Airy Bi function at z

airyBiPrimex: JLFloat64 -> JLFloat64

airyBiPrimex(z) computes scaled derivative of the Airy Bi function at z

airyBix: JLFloat64 -> JLFloat64

airyBix(z) computes scaled Airy Bi function at z

besselI: (JLFloat64, JLFloat64) -> JLFloat64

besselI(nu,z) computes modified Bessel function of the first kind of order nu at z

besselIx: (JLFloat64, JLFloat64) -> JLFloat64

besselIx(nu,z) computes scaled modified Bessel function of the first kind of order nu at z

besselJ0: JLFloat64 -> JLFloat64

besselJ0(z) computes besselj(0,z)

besselJ1: JLFloat64 -> JLFloat64

besselJ1(z) computes besselj(1,z)

besselJ: (JLFloat64, JLFloat64) -> JLFloat64

besselJ(nu,z) computes Bessel function of the first kind of order nu at z

besselJx: (JLFloat64, JLFloat64) -> JLFloat64

besselJx(nu,z) computes scaled Bessel function of the first kind of order nu at z

besselK: (JLFloat64, JLFloat64) -> JLFloat64

besselK(nu,z) computes modified Bessel function of the second kind of order nu at z

besselKx: (JLFloat64, JLFloat64) -> JLFloat64

besselKx(nu,z) computes scaled modified Bessel function of the second kind of order nu at z

besselY0: JLFloat64 -> JLFloat64

besselY0(z) computes bessely(0,z)

besselY1: JLFloat64 -> JLFloat64

besselY1(z) computes bessely(1,z)

besselY: (JLFloat64, JLFloat64) -> JLFloat64

besselY(nu,z) computes Bessel function of the second kind of order nu at z

besselYx: (JLFloat64, JLFloat64) -> JLFloat64

besselYx(nu,z) computes scaled Bessel function of the second kind of order nu at z

Beta: (JLFloat64, JLFloat64) -> JLFloat64

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

Ci: JLFloat64 -> JLFloat64

Ci(x) computes cosine integral Ci(x)

dawson: JLFloat64 -> JLFloat64

dawson(x) computes scaled imaginary error function, a.k.a. Dawson function.

digamma: JLFloat64 -> JLFloat64

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

Ei: JLFloat64 -> JLFloat64

Ei(x) computes exponential integral Ei(x)

ellipticE: JLFloat64 -> JLFloat64

ellipticE(m) computes complete elliptic integral of 2nd kind E(m)

ellipticK: JLFloat64 -> JLFloat64

ellipticK(m) computes complete elliptic integral of 1st kind K(m)

erf: (JLFloat64, JLFloat64) -> JLFloat64

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

erf: JLFloat64 -> JLFloat64

erf(x) computes error function at x

erfc: JLFloat64 -> JLFloat64

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

erfcx: JLFloat64 -> JLFloat64

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

erfi: JLFloat64 -> JLFloat64

erfi(x) computes imaginary error function defined as -i erf(ix)

eta: JLFloat64 -> JLFloat64

eta(x) computes Dirichlet eta function at x

expint: (JLFloat64, JLFloat64) -> JLFloat64

expint(nu, z) computes exponential integral function

expintx: JLFloat64 -> JLFloat64

expintx(x) computes scaled exponential integral function

Gamma: (JLFloat64, JLFloat64) -> JLFloat64

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

Gamma: JLFloat64 -> JLFloat64

Gamma(z) computes Gamma function Gamma(z)

gamma_inc_inv: (JLFloat64, JLFloat64, JLFloat64) -> JLFloat64

gamma_inc_inv(a,p,q) computes inverse of incomplete gamma function ratio P(a,x) and Q(a,x) (i.e evaluates x given P(a,x)=p and Q(a,x)=q)

hankelH1: (JLFloat64, JLFloat64) -> JLFloat64

hankelH1(nu,z) computes besselh(nu, 1, z)

hankelH1x: (JLFloat64, JLFloat64) -> JLFloat64

hankelH1x(nu,z) computes scaled besselh(nu, 1, z)

hankelH2: (JLFloat64, JLFloat64) -> JLFloat64

hankelH2(nu,z) computes besselh(nu, 2, z)

hankelH2x: (JLFloat64, JLFloat64) -> JLFloat64

hankelH2x(nu,z) computes scaled besselh(nu, 2, z)

invdigamma: JLFloat64 -> JLFloat64

invdigamma(x) computes invdigamma function (i.e. inverse of digamma function at x using fixed-point iteration algorithm)

inverseErf: JLFloat64 -> JLFloat64

inverseErf(x) computes inverse function of erf()

inverseErfc: JLFloat64 -> JLFloat64

inverseErfc(x) computes inverse function of erfc.

jinc: JLFloat64 -> JLFloat64

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

logabsbeta: (JLFloat64, JLFloat64) -> JLFloat64

logabsbeta(x,y) computes accurate log(abs(beta(x,y))) for large x or y

logabsgamma: JLFloat64 -> JLFloat64

logabsgamma(x) computes accurate log(abs(gamma(x))) for large x

logBeta: (JLFloat64, JLFloat64) -> JLFloat64

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

logerfc: JLFloat64 -> JLFloat64

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

logerfcx: JLFloat64 -> JLFloat64

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

logGamma: (JLFloat64, JLFloat64) -> JLFloat64

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

logGamma: JLFloat64 -> JLFloat64

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

polygamma: (JLInt64, JLFloat64) -> JLFloat64

polygamma(m,x) computes polygamma function (i.e the (m+1)-th derivative of the loggamma function at x)

riemannZeta: JLFloat64 -> JLFloat64

riemannZeta(x) computes Riemann zeta function at x

Si: JLFloat64 -> JLFloat64

Si(x) computes sine integral Si(x)

sphericalBesselJ: (JLFloat64, JLFloat64) -> JLFloat64

sphericalBesselJ(nu,z) computes Spherical Bessel function of the first kind of order nu at z

sphericalBesselY: (JLFloat64, JLFloat64) -> JLFloat64

sphericalBesselY(nu,z) computes Spherical Bessel function of the second kind of order nu at z

trigamma: JLFloat64 -> JLFloat64

trigamma(x) computes trigamma function (i.e the logarithmic second derivative of gamma at x)