Rather complicated sum with high values for both i and m

SIUHON

New member
Joined
Jul 21, 2018
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Hello everybody,

The sum I am dealing with is:


Σ (i=5.483132598*1018; m=2*1037) a [b∶ √(1 - c/(d n2 +c))]3


a, b, c, d represent groups of physical constants. This can be further simplified to:


Σ (i=5.483132598*1018; m=2*1037) a (b∶ √(1 - 1/(d' n2 +1)))3


With d' = d/c. And then to:


a * b3 * ∑ (...) (1 - 1/(d'n2 + 1))-3/2


For values of d'n^2 which are smaller than 1, we can use this approximation:


∑ (...) = a b3 d'-3/2 ζ(3)


But that is not a big help I think. Is there any way to approach this sum through integrals?


Thank you in advance!
 
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