RandomFieldsUtils (version 0.0.1)

Struve: Modified Struve functions and related functions

Description

These functions return the values of the modified Struve functions and related functions

Usage

struveH(x, nu) 
struveL(x, nu, expon.scaled=FALSE)
I0L0(x)

Arguments

x

non-negative numeric vector

nu

numeric vector

expon.scaled

logical; if TRUE, the results are exponentially scaled in order to avoid overflow or underflow respectively.

Value

• Numeric vector with the (scaled, if expon.scaled = TRUE) values of the corresponding function. The length of the result is the maximum of the lengths of the arguments x and nu. The two arguments are recycled to that length.

Details

I0L0 returns besselI(nu=0) minus struveL(nu=0).

References

• MacLeod, A.J. (1993) Chebyshev expansions for modified Struve and related functions,Mathematics of Computation,60, 735-747
• Abramowitz, M., and Stegun, I.A. (1984)Pocketbook of Mathematical Functions, Verlag Harry Deutsch

See Also

besselI

Examples

x <- seq(1, 2, 0.1)
struveH(x, 0)
struveH(x, 1)

I0L0(x) - (besselI(x, nu=0) - struveL(x, 0)) 
besselI(x, nu=1) - struveL(x, 1) ## cf. Abramovitz & Stegun, table 12.1