Not Catalan's Constant

Calculus Level 5

n=0(1)n(2n+1)3=πAB \large \displaystyle \sum_{n=0}^{\infty} \dfrac{(-1)^n}{(2n+1)^3} = \dfrac{\pi^A}{B}

If the equation holds true for positive integers AA and BB, find A+BA+B.

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