DPQ (version 0.3-3)

logcf: Continued Fraction Approximation of Log-Related Series

Description

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

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")
# }

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