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Odd Power


An odd power is a number of the form m^n for m>0 an integer and n a positive odd integer. The first few odd powers are 1, 8, 27, 32, 64, 125, 128, 216, 243, 343, 512, ... (OEIS A070265). Amazingly, the double series of reciprocals of the odd powers that are congruent to 3 (mod 4) is given by

 sum_(n=0)^inftysum_(m=1)^infty1/((4n+3)^(2m+1))=1/8pi-1/2ln2.

See also

Perfect Power, Power

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References

Sloane, N. J. A. Sequence A070265 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Odd Power

Cite this as:

Weisstein, Eric W. "Odd Power." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OddPower.html

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