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ecd (version 0.9.2.4)

ecld.gamma: Incomplete gamma function and asymptotic expansion

Description

ecld.gamma is the wrapper for incomplete gamma function \(\Gamma(s,x)\). It is mainly to wrap around pgamma. And ecld.gamma_hgeo is the asymptotic expansion of \(\Gamma(s,x)\) using hypergeometric series, \(e^{-x} x^{s-1} {}_2 F_0 (1,1-s;;-1/x)\). It is mainly used in for star OGF \(L^{*}(k;\lambda)\). ecld.gamma_2F0 is simply \({}_2 F_0 (1,1-s;;-1/x)\), which is used in the star OGF expansion.

Usage

ecld.gamma(s, x = 0, na.stop = TRUE)

ecld.gamma_hgeo(s, x, order)

ecld.gamma_2F0(s, x, order)

Arguments

s

numeric vector, for the order of incomplete gamma function

x

numeric or MPFR vector

na.stop

logical, stop if NaN is generated. The default is TRUE.

order

numeric, the order of the power series

Value

numeric