DoubleFloatSpecialFunctions

special.spad line 1 [edit on github]

This package provides special functions for double precision real and complex floating point.

besselI: (Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

besselI(v, x) is the modified Bessel function of the first kind, I(v, x). This function satisfies the differential equation: x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0.

besselI: (DoubleFloat, DoubleFloat) -> DoubleFloat

besselI(v, x) is the modified Bessel function of the first kind, I(v, x). This function satisfies the differential equation: x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0.

besselJ: (Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

besselJ(v, x) is the Bessel function of the first kind, J(v, x). This function satisfies the differential equation: x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0.

besselJ: (DoubleFloat, DoubleFloat) -> DoubleFloat

besselJ(v, x) is the Bessel function of the first kind, J(v, x). This function satisfies the differential equation: x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0.

besselK: (Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

besselK(v, x) is the modified Bessel function of the second kind, K(v, x). This function satisfies the differential equation: x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0. Note: The default implementation uses the relation K(v, x) = \%pi/2*(I(-v, x) - I(v, x))/sin(v*\%pi) so is not valid for integer values of v.

besselK: (DoubleFloat, DoubleFloat) -> DoubleFloat

besselK(v, x) is the modified Bessel function of the second kind, K(v, x). This function satisfies the differential equation: x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0. Note: The default implementation uses the relation K(v, x) = \%pi/2*(I(-v, x) - I(v, x))/sin(v*\%pi). so is not valid for integer values of v.

besselY: (Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

besselY(v, x) is the Bessel function of the second kind, Y(v, x). This function satisfies the differential equation: x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0. Note: The default implementation uses the relation Y(v, x) = (J(v, x) cos(v*\%pi) - J(-v, x))/sin(v*\%pi) so is not valid for integer values of v.

besselY: (DoubleFloat, DoubleFloat) -> DoubleFloat

besselY(v, x) is the Bessel function of the second kind, Y(v, x). This function satisfies the differential equation: x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0. Note: The default implementation uses the relation Y(v, x) = (J(v, x) cos(v*\%pi) - J(-v, x))/sin(v*\%pi) so is not valid for integer values of v.

digamma: Complex DoubleFloat -> Complex DoubleFloat

digamma(x) is the function, psi(x), defined by psi(x) = Gamma'(x)/Gamma(x).

polygamma: (NonNegativeInteger, Complex DoubleFloat) -> Complex DoubleFloat

polygamma(n, x) is the n-th derivative of digamma(x).