Description Usage Arguments Details Value Author(s) References See Also Examples
Compute Bessel functions I[nu](x) and K[nu](x) for large nu and possibly large x, using asymptotic expansions in Debye polynomials.
1 2 | besselI.nuAsym(x, nu, k.max, expon.scaled = FALSE, log = FALSE)
besselK.nuAsym(x, nu, k.max, expon.scaled = FALSE, log = FALSE)
|
x |
numeric or |
nu |
numeric; The order (maybe fractional!) of the corresponding Bessel function. |
k.max |
integer number of terms in the expansion. Must be in
|
expon.scaled |
logical; if |
log |
logical; if TRUE, log(f(.)) is returned instead of f. |
Abramowitz & Stegun , page 378, has formula 9.7.7 and 9.7.8 for the asymptotic expansions of I_{ν}(x) and K_{ν}(x), respectively, also saying When nu -> oo, these expansions (of I[nu](nu * z) and K[nu](nu * z)) hold uniformly with respect to z in the sector |arg z| <= pi/2 - eps, where eps iw qn arbitrary positive number. and for this reason, we require Re(x) >= 0.
The Debye polynomials u_k(x) are defined in 9.3.9 and 9.3.10 (page 366).
a numeric vector of the same length as the long of x
and
nu
. (usual argument recycling is applied implicitly.)
Martin Maechler
Abramowitz, M., and Stegun, I. A. (1955, etc). Handbook of mathematical functions (NBS AMS series 55, U.S. Dept. of Commerce), pp. 366, 378.
From this package Bessel: BesselI()
; further,
besselIasym()
for the case when x is large and
ν is small or moderate.
Further, from base: besselI
, etc.
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