DPQ (version 0.4-1)

logcf: Continued Fraction Approximation of Log-Related Series

Description

Compute a continued fraction approximation to the series (infinite sum) $$\sum _{k=0}^{\mathrm{\infty }}\frac{x^k}{i+k\cdot d}=\frac{1}{i}+\frac{x}{i+d}+\frac{x^2}{i+2\ast d}+\frac{x^3}{i+3\ast d}+\dots$$

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.

See Also

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

Examples

# NOT RUN {
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")
# }