I need to calculate a coefficient as follows

coef[a_, j_] := 
   NSum[(a/Sqrt[2])^n 1/Sqrt[((n - j)!) (j!)], {n, j, Infinity}]

This coefficient is an infinite sum over n and depends on a real number a and an index j.

I choose a = 2, and j = 19, i.e. coef[2,19], I get the outcome


but when I calculate coef[2,20] (j=20) the program runs forever.

How can I resolve this problem?

  • 3
    $\begingroup$ Welcome to MSE! Change definition to coef[a_?NumericQ, j_?NumericQ] := E^(-a^2/2)*NSum[(a/Sqrt[2])^n 1/Sqrt[((n - j)!) (j!)], {n, j, Infinity}] and it will compute immediately. $\endgroup$
    – Alx
    Dec 18, 2019 at 12:00
  • $\begingroup$ @Alx: Thank you. So simple but definitely works. $\endgroup$ Dec 19, 2019 at 12:28
  • $\begingroup$ @Alx Please could you explain why it works? Or, to put in a different way the question I'm really interested in, "What problem prevented the equation being solved, and how does your solution overcome that problem?" $\endgroup$ Mar 30, 2023 at 10:20


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