# logcf

From DPQ v0.3-3
by Martin Maechler

##### Continued Fraction Approximation of Log-Related Series

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

- Keywords
- math

##### 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`

....

##### 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")
# }
```

*Documentation reproduced from package DPQ, version 0.3-3, License: GPL (>= 2)*

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