RandomFieldsUtils (version 0.5.3)

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

# NOT RUN {
if (FALSE) {

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

}

# }

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