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Solving a Triple Infinite Series with an Exponential Integral

Tags: math , Gamma Integral , Hyperbolic Functions , Combinatorics , Mathematical Analysis , Improper Integral , Triple Summation , Calculus , Infinite Series

Published July 9, 2026, 7:46 p.m. by james

The value is:

$$ \boxed{\frac{94}{375}} $$

We have

$$ S = \sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \sum_{c=1}^{\infty} \int_0^\infty \frac{x^{a+b+c}}{(a+b+c)!} e^{-4x}\cosh(2x)\,dx $$ …