combfunc.spad line 443 [edit on github]
Provides some special functions over an integral domain.
Beta(x, y) returns the beta function applied to x and y.
Beta(x, a, b) is incomplete Beta function applied to x, a and b.
Gamma(f) returns the formal Gamma function applied to f.
Gamma(a, x) returns the incomplete Gamma function applied to a and x.
abs(f) returns the absolute value operator applied to f.
airyAi(x) returns the Airy Ai function applied to x.
airyAiPrime(x) returns the derivative of Airy Ai function applied to x.
airyBi(x) returns the Airy Bi function applied to x.
airyBiPrime(x) returns the derivative of Airy Bi function applied to x.
angerJ(v, z) is the Anger J function.
belong?(op) returns true if op is a special function operator.
besselI(x, y) returns the Bessel I function applied to x and y.
besselJ(x, y) returns the Bessel J function applied to x and y.
besselK(x, y) returns the Bessel K function applied to x and y.
besselY(x, y) returns the Bessel Y function applied to x and y.
ceiling(x) returns the smallest integer above or equal x.
charlierC(n, a, z) is the Charlier polynomial.
coerce_Q(x) should be local but conditional
conjugate(f) returns the conjugate value operator applied to f.
digamma(x) returns the digamma function applied to x.
diracDelta(x) is unit mass at zeros of x.
ellipticE(m) is the complete elliptic integral of the second kind: ellipticE(m) = integrate(sqrt(1-m*t^2)/sqrt(1-t^2), t = 0..1).
ellipticE(z, m) is the incomplete elliptic integral of the second kind: ellipticE(z, m) = integrate(sqrt(1-m*t^2)/sqrt(1-t^2), t = 0..z).
ellipticF(z, m) is the incomplete elliptic integral of the first kind : ellipticF(z, m) = integrate(1/sqrt((1-t^2)*(1-m*t^2)), t = 0..z).
ellipticK(m) is the complete elliptic integral of the first kind: ellipticK(m) = integrate(1/sqrt((1-t^2)*(1-m*t^2)), t = 0..1).
ellipticPi(z, n, m) is the incomplete elliptic integral of the third kind: ellipticPi(z, n, m) = integrate(1/((1-n*t^2)*sqrt((1-t^2)*(1-m*t^2))), t = 0..z).
floor(x) returns the largest integer below or equal x.
fractionPart(x) returns the fractional part of x.
hahnQ(n, a, b, N, z) is the Hahn polynomial.
hahnR(n, c, d, N, z) is the dual Hahn polynomial.
hahnS(n, a, b, c, z) is the continuous dual Hahn polynomial.
hahn_p(n, a, b, bar_a, bar_b, z) is the continuous Hahn polynomial.
hankelH1(v, z) is first Hankel function (Bessel function of the third kind).
hankelH2(v, z) is the second Hankel function (Bessel function of the third kind).
hermiteH(n, z) is the Hermite polynomial.
hypergeometricF(la, lb, z) is the generalized hypergeometric function.
iAiryAi(x) should be local but conditional.
iAiryAiPrime(x) should be local but conditional.
iAiryBi(x) should be local but conditional.
iAiryBiPrime(x) should be local but conditional.
iLambertW(x) should be local but conditional.
iiAiryAi(x) should be local but conditional.
iiAiryAiPrime(x) should be local but conditional.
iiAiryBi(x) should be local but conditional.
iiAiryBiPrime(x) should be local but conditional.
iiBesselI(x) should be local but conditional.
iiBesselJ(x) should be local but conditional.
iiBesselK(x) should be local but conditional.
iiBesselY(x) should be local but conditional.
iiBeta(x) should be local but conditional.
iiGamma(x) should be local but conditional.
iiHypergeometricF(l) should be local but conditional.
iiPolylog(x, s) should be local but conditional.
iiabs(x) should be local but conditional.
iiconjugate(x) should be local but conditional.
iidigamma(x) should be local but conditional.
iipolygamma(x) should be local but conditional.
jacobiCn(z, m) is the Jacobi elliptic cn function, defined by jacobiCn(z, m)^2 + jacobiSn(z, m)^2 = 1 and jacobiCn(0, m) = 1.
jacobiDn(z, m) is the Jacobi elliptic dn function, defined by jacobiDn(z, m)^2 + m*jacobiSn(z, m)^2 = 1 and jacobiDn(0, m) = 1.
jacobiP(n, a, b, z) is the Jacobi polynomial.
jacobiSn(z, m) is the Jacobi elliptic sn function, defined by the formula jacobiSn(ellipticF(z, m), m) = z.
jacobiTheta(z, m) is the Jacobi Theta function in Jacobi notation.
jacobiZeta(z, m) is the Jacobi elliptic zeta function, defined by D(jacobiZeta(z, m), z) = jacobiDn(z, m)^2 - ellipticE(m)/ellipticK(m) and jacobiZeta(0, m) = 0.
kelvinBei(v, z) is the Kelvin bei function defined by equality. kelvinBei(v, z) = imag(besselJ(v, exp(3*%pi*%i/4)*z)). for z and v real.
kelvinBer(v, z) is the Kelvin ber function defined by equality kelvinBer(v, z) = real(besselJ(v, exp(3*%pi*%i/4)*z)) for z and v real.
kelvinKei(v, z) is the Kelvin kei function defined by equality kelvinKei(v, z) = imag(exp(-v*%pi*%i/2)*besselK(v, exp(%pi*%i/4)*z)) for z and v real.
kelvinKer(v, z) is the Kelvin kei function defined by equality kelvinKer(v, z) = real(exp(-v*%pi*%i/2)*besselK(v, exp(%pi*%i/4)*z)) for z and v real.
krawtchoukK(n, p, N, z) is the Krawtchouk polynomial.
kummerM(a, b, z) is the Kummer M function.
kummerU(a, b, z) is the Kummer U function.
laguerreL(n, a, z) is the Laguerre polynomial.
lambertW(x) is the Lambert W function at x.
legendreP(nu, mu, z) is the Legendre P function.
legendreQ(nu, mu, z) is the Legendre Q function.
lerchPhi(z, s, a) is the Lerch Phi function.
lommelS1(mu, nu, z) is the Lommel s function.
lommelS2(mu, nu, z) is the Lommel S function.
meijerG(la, lb, lc, ld, z) is the meijerG function.
meixnerM(n, b, c, z) is the Meixner polynomial.
meixnerP(n, phi, lambda, z) is the Meixner-Pollaczek polynomial.
operator(op) returns a copy of op with the domain-dependent properties appropriate for F; error if op is not a special function operator.
polygamma(x, y) returns the polygamma function applied to x and y.
polylog(s, x) is the polylogarithm of order s at x.
racahR(n, a, b, c, d, z) is the Racah polynomial.
retract_Q(x) should be local but conditional
riemannZeta(z) is the Riemann Zeta function.
sign(x) returns the sign of x.
struveH(v, z) is the Struve H function.
struveL(v, z) is the Struve L function defined by the formula struveL(v, z) = -%i^exp(-v*%pi*%i/2)*struveH(v, %i*z).
unitStep(x) is 0 for x less than 0, 1 for x bigger or equal 0.
weberE(v, z) is the Weber E function.
weierstrassP(g2, g3, x) is the Weierstrass P function.
weierstrassPInverse(g2, g3, z) is the inverse of Weierstrass P function, defined by the formula weierstrassP(g2, g3, weierstrassPInverse(g2, g3, z)) = z.
weierstrassPPrime(g2, g3, x) is the derivative of Weierstrass P function.
weierstrassSigma(g2, g3, x) is the Weierstrass Sigma function.
weierstrassZeta(g2, g3, x) is the Weierstrass Zeta function.
whittakerM(k, m, z) is the Whittaker M function.
whittakerW(k, m, z) is the Whittaker W function.
wilsonW(n, a, b, c, d, z) is the Wilson polynomial.