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Zeta annuities, fractional calculus, and polylogarithms

Tao, Jim (2022): Zeta annuities, fractional calculus, and polylogarithms.

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Abstract

We derive the present value and accumulated value formulas for zeta annuities-immediate, due, and continuously payable for all real values of s. Taking the limit n → ∞, the annuities become perpetuities, and the present value formula for a zeta perpetuity-immediate coincides with the polylogarithm.

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