Double summation continues

Calculus Level 5

\[\displaystyle \sum_{m=1}^{\infty} \sum_{k=0}^{\infty} \dfrac{(-1)^m}{(2k + 1)^2 + m^2} = \dfrac{\pi \text{ ln } a - \pi^b}{c^d}\]

  • Find \(13\times(a + b + c + d)\)

  • \(a,b,c\) are prime numbers and \(d\) is an integer

  • \( \text{ ln } \)- natural logarithm

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