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In NIST equation 8.20.2 what is meant by $(p)_{k}$

$$\mathop{E_{p}}\nolimits\!\left(z\right)\sim\frac{e^{-z}}{z}\sum_{k=0}^{% \infty}(-1)^{k}\frac{\left(p\right)_{k}}{z^{k}},$$

sky-light
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1 Answers1

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This is the Pochhammer symbol defined in http://dlmf.nist.gov/5.2.iii $$(p)_k = p\cdot(p+1)\cdot(p+1)\dots(p+k-1)=\frac{\Gamma(p+k)}{\Gamma(p)}$$

gammatester
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  • as you know the limits of the $sum$ is from $0 to \infty$, but if I choose large number I will not get better result, however, if I choose small number the result looks much better. what is the reason behind that? – sky-light Oct 22 '14 at 15:22
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    This is an asymptotic expansion, not a convergent series. With AE you normally use only a few terms, and often there are error estimates (see eg the well-known Stirling AE for the Gamma function). In your case there is no error term listed, but I guess you can compute one from http://dlmf.nist.gov/8.20.E1. – gammatester Oct 23 '14 at 06:56