I wanted to expand a function of $x$ about $x=\infty$ and see its coefficients as a function of the parameters $m,n,q,y$ and I wrote this - but it didn't work!
It gave me back a very complicated expression with powers of $x$ scattered everywhere - but I want a Laurent series expansion of it!
Can someone kindly help with this?
Assuming [ y ∈ Reals && m ∈ Reals && q > 0 && n ∈ Integers && x > 0 , Series [ ((
Gamma [ I x + (1 + y)/2] Gamma [ -I x + (1 + y)/2] )/(
Gamma [I x] Gamma [ -I x] ) )* (1/(
x^2 + m^2 + (n/q)^2)), {x, Infinity, 3}] ]
To write it readably - the function is, $\frac{ \Gamma (ix + (1+y)/2) \Gamma( -ix + (1+y)/2)}{\Gamma (- i x) \Gamma (i x) } \frac{1}{x^2 + m^2 + (n/q)^2 }$
On some computers and Mathematica versions - the answer to the above comes out as -
(1/x)^-y (1/x+(2 π (-m^2/(2 π)-n^2/(2 π q^2))+1/24 (-y +y^3)) (1/x)^3+O[1/x]^4)
but I don't know why on my computer and Mathematica it doesn'!
Some simple examples do work like Series [ x/(x^2 + 3) , {x, Infinity, 2}]