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!
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!