calculate-n-0-1-n-2-

Question Number 140978 by Mathspace last updated on 14/May/21

c a l c u l a t e \sum_{n = 0}^{\infty} \frac{1}{{(n!)}^{2}}

Answered by Dwaipayan Shikari last updated on 14/May/21

\underset{n = 0}{\sum^{\infty}} \frac{1}{n! n!} = \underset{n = 0}{\sum^{\infty}} \frac{{(1)}_{n}^{2}}{{(1)}_{n}^{3} n!} {(1)}^{n} =_{2} F_{3} (1, 1; 1; 1; 1; 1)