Re: PolyGamma - series expansions
- To: mathgroup at smc.vnet.net
- Subject: [mg41707] Re: PolyGamma - series expansions
- From: "Tom Hardy" <tomhardy at sdc.cox.net>
- Date: Mon, 2 Jun 2003 04:35:17 -0400 (EDT)
- References: <bb50aj$4b1$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Series[PolyGamma[n], {n, Infinity, 2}]/.n ->2 n;
Series[PolyGamma[n], {n, Infinity, 2}]/.n->n+2;
"dougaler" <dougaler at uboot.com> wrote in message
news:bb50aj$4b1$1 at smc.vnet.net...
> I want to expand lots of things like
> (Gamma[n+f[s]])^(-1) D[ Gamma[n+f[s]] ,s] as n->Infinty
>
> Mathematica gives an asymptotic power series for the digamma function:
>
> In: Series[PolyGamma[n], {n, Infinity, 2}]
> Out: -Log[1/n]-1/2n+O[1/n^2]
>
> However, it does not like:
>
> Series[PolyGamma[2n], {n, Infinity, 2}]
> or
> Series[PolyGamma[n+2], {n, Infinity, 2}]
>
> Can anyone tell me why this is or suggest any neat remedies?
>
> Thanks very much.
>