# Bug in Series[Pochhammer[1+n, n], {n,Infinity,1}]?

The function

  Pochhammer[1 + n, n]


tends to infinity. We have

  FunctionExpand[Pochhammer[1 + n, n]]
(* (2^(2*n)*Gamma[1/2 + n])/Sqrt[Pi] *)


But following result

  Series[Pochhammer[1 + n, n] , {n, Infinity, 1}]
(* 1 + O[1/n]^2 *)


is a bug! Tested under versions 10.2 and 7.0, same results. Interesting is that

  Limit[Pochhammer[1 + n, n]/(2^(2*n + 1/2)*n^n/E^n), n -> Infinity]


is correct.

• What is your question here? Have you reported this behavior to Wolfram support? – MarcoB Apr 24 '16 at 4:50
• About bugs please see mathematica.stackexchange.com/questions/84077/… The bug was fixed only after I put the question here... – Vaclav Kotesovec Apr 24 '16 at 6:06
• Question is: please confirm that it is a bug and test it in other versions. – Vaclav Kotesovec Apr 24 '16 at 6:10
• Of course, the workaround is to use Series[] on the gamma function expression instead. Anyway, 5.2 does not have the bug, but 10.4.1 does. – J. M. will be back soon Apr 24 '16 at 13:34
• I wonder if MMA is actually being smart, figuring out that there is no Taylor Series at infinity, and instead giving the MacClaurin series for the singuarity "at infinity". Note that for simple poles, (e.g., Series[1/Sin[x], {x, 2 Pi, 5}]), it does find the negative power, though it doesn't include anything like O[1/x]^2. ...just a thought. – Paco Jain Apr 25 '16 at 19:41