trigcat.spad line 235 [edit on github]
Category for the other special functions.
Beta(x, y) is Gamma(x) * Gamma(y)/Gamma(x+y).
Beta(x, a, b) is the incomplete Beta function.
Gamma(x) is the Euler Gamma function.
Gamma(a, x) is the incomplete Gamma function.
abs(x) returns the absolute value of x.
airyAi(x) is the Airy function Ai(x)
airyAiPrime(x) is the derivative of the Airy function Ai(x)
airyBi(x) is the Airy function Bi(x)
airyBiPrime(x) is the derivative of the Airy function Bi(x)
angerJ(v, z) is the Anger J function.
besselI(v, z) is the modified Bessel function of the first kind.
besselJ(v, z) is the Bessel function of the first kind.
besselK(v, z) is the modified Bessel function of the second kind.
besselY(v, z) is the Bessel function of the second kind.
ceiling(x) returns the smallest integer above or equal x.
charlierC(n, a, z) is the Charlier polynomial.
conjugate(x) returns the conjugate of x.
digamma(x) is the logarithmic derivative of Gamma(x) (often written psi(x) in the literature).
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. Note: fractionPart(x) = x - floor(x).
hahnQ(n, a, b, N, z) s 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.
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(mu, nu, z) is the Kummer M function.
kummerU(mu, nu, z) is the Kummer U function.
laguerreL(n, a, z) is the Laguerre polynomial.
lambertW(z) = w is the principal branch of the solution to the equation we^w = z.
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.
polygamma(k, x) is the k-th derivative of digamma(x), (often written psi(k, x) in the literature).
polylog(s, x) is the polylogarithm of order s at x.
racahR(n, a, b, c, d, z) is the Racah polynomial.
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, z) 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, z) is the derivative of Weierstrass P function.
weierstrassSigma(g2, g3, z) is the Weierstrass Sigma function.
weierstrassZeta(g2, g3, z) 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.