I have a following expression $$ f=\Pi_{i=1}^n \left[ 1 + \frac{1}{t} +\frac{ (m+i)}{t^2} +\frac{ (m+i)^2}{t^3} + \cdots \right] $$ here $m,n,t$ are positive integers.
I want to obtain a series expansion for $f$ as $1/t,1/t^2,1/t^3,\cdots$ up to maybe $1/t^6$. A general expression for any order is not needed.
I used
f = \!\(
\*UnderoverscriptBox[\(\[Product]\), \(i = 1\), \(n\)]\((1 +
\*FractionBox[\(1\), \(t\)] +
\*FractionBox[\((m + i)\), \(t^2\)] +
\*FractionBox[\(\((m + i)\)^2\), \(t^3\)])\)\)
Series[f, {t, Infinity, 3}, Assumptions -> Element[m, Integers]]
Mathematica 7.0 gives me a complicated expression including Arg
, Floor
, Csc
, etc.
Is there any way to obtain simple expression? I can do low order by hand, but for high order, it is increasingly complicated..
Series
function?%
just refers to the prior evaluation, and we don't know exactly what you've done. $\endgroup$ – Verbeia Oct 16 '14 at 4:11