Sum of Reciprocals of Cubes of Odd Integers Alternating in Sign in Pairs
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This theorem requires a proof..
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Theorem
| \(\displaystyle \frac 1 {1^3} + \frac 1 {3^3} - \frac 1 {5^3} - \frac 1 {7^3} + \cdots\) | \(=\) | \(\displaystyle \frac {3 \pi^3 \sqrt 2} {128}\) |
Proof
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Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 19$: Series involving Reciprocals of Powers of Positive Integers: $19.29$
