logcf {DPQ}R Documentation

Continued Fraction Approximation of Log-Related Series

Description

Compute a continued fraction approximation to the series (infinite sum)

sum(k=0,...,Inf; x^k/(i+k*d)) = 1/i + x/(i+d) + x^2/(i+2*d) + x^3/(i+3*d) + ...

Needed as auxiliary function in log1pmx() and lgamma1p().

Usage

logcf(x, i, d, eps, maxit = 10000)

Arguments

x

numeric vector

i

positive numeric

d

non-negative numeric

eps

positive number, the convergence tolerance.

maxit

a positive integer, the maximal number of iterations or terms in the truncated series used.

Value

a numeric vector with the same attributes as x.

Note

Rescaling is done by (namespace hidden) “global” scalefactor ....

Author(s)

Martin Maechler, based on ....

See Also

lgamma1p, log1pmx, and pbeta, whose prinicipal algorithm has evolved from TOMS 708.

Examples

l32 <- curve(logcf(x, 3,2, eps=1e-7), -3, 1)
abline(h=0,v=1, lty=3, col="gray50")
plot(y~x, l32, log="y", type = "o", main = "logcf(*, 3,2)  in log-scale")

[Package DPQ version 0.4-2 Index]