JuliaFloat32SpecialFunctions2

jf32sf2.spad line 1 [edit on github]

Special functions computed using Julia's ecosystem. They are here essentially for “completeness” purpose with JuliaFloat32. You should use the DoubleFloat's special functions if available, calling Julia functions is costly.

airyAi: JuliaFloat32 -> JuliaFloat32

airyAi(z) computes Airy Ai function at z

airyAiPrime: JuliaFloat32 -> JuliaFloat32

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

airyAiPrimex: JuliaFloat32 -> JuliaFloat32

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

airyAix: JuliaFloat32 -> JuliaFloat32

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

airyBi: JuliaFloat32 -> JuliaFloat32

airyBi(z) computes Airy Bi function at z

airyBiPrime: JuliaFloat32 -> JuliaFloat32

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

airyBiPrimex: JuliaFloat32 -> JuliaFloat32

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

airyBix: JuliaFloat32 -> JuliaFloat32

airyBix(z) computes scaled Airy Bi function at z

besselI: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

besselIx: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

besselJ0: JuliaFloat32 -> JuliaFloat32

besselJ0(z) computes besselj(0,z)

besselJ1: JuliaFloat32 -> JuliaFloat32

besselJ1(z) computes besselj(1,z)

besselJ: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

besselJx: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

besselK: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

besselKx: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

besselY0: JuliaFloat32 -> JuliaFloat32

besselY0(z) computes bessely(0,z)

besselY1: JuliaFloat32 -> JuliaFloat32

besselY1(z) computes bessely(1,z)

besselY: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

besselYx: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

Beta: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

Ci: JuliaFloat32 -> JuliaFloat32

Ci(x) computes cosine integral Ci(x)

dawson: JuliaFloat32 -> JuliaFloat32

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

digamma: JuliaFloat32 -> JuliaFloat32

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

Ei: JuliaFloat32 -> JuliaFloat32

Ei(x) computes exponential integral Ei(x)

ellipticE: JuliaFloat32 -> JuliaFloat32

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

ellipticK: JuliaFloat32 -> JuliaFloat32

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

erf: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

erf: JuliaFloat32 -> JuliaFloat32

erf(x) computes error function at x

erfc: JuliaFloat32 -> JuliaFloat32

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

erfcx: JuliaFloat32 -> JuliaFloat32

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

erfi: JuliaFloat32 -> JuliaFloat32

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

eta: JuliaFloat32 -> JuliaFloat32

eta(x) computes Dirichlet eta function at x

expint: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

expint(nu, z) computes exponential integral function

expintx: JuliaFloat32 -> JuliaFloat32

expintx(x) computes scaled exponential integral function

Gamma: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

Gamma: JuliaFloat32 -> JuliaFloat32

Gamma(z) computes Gamma function Gamma(z)

gamma_inc_inv: (JuliaFloat32, JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

hankelH1x: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

hankelH2: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

hankelH2x: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

invdigamma: JuliaFloat32 -> JuliaFloat32

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

inverseErf: JuliaFloat32 -> JuliaFloat32

inverseErf(x) computes inverse function of erf()

inverseErfc: JuliaFloat32 -> JuliaFloat32

inverseErfc(x) computes inverse function of erfc.

jinc: JuliaFloat32 -> JuliaFloat32

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

logabsbeta: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

logabsgamma: JuliaFloat32 -> JuliaFloat32

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

logBeta: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

logerfc: JuliaFloat32 -> JuliaFloat32

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

logerfcx: JuliaFloat32 -> JuliaFloat32

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

logGamma: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

logGamma: JuliaFloat32 -> JuliaFloat32

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

polygamma: (JuliaInt64, JuliaFloat32) -> JuliaFloat32

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

riemannZeta: JuliaFloat32 -> JuliaFloat32

riemannZeta(x) computes Riemann zeta function at x

Si: JuliaFloat32 -> JuliaFloat32

Si(x) computes sine integral Si(x)

sphericalBesselJ: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

sphericalBesselY: (JuliaFloat32, JuliaFloat32) -> JuliaFloat32

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

trigamma: JuliaFloat32 -> JuliaFloat32

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