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Zeta annuities, fractional calculus, and polylogarithms

Author

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  • Tao, Jim

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.

Suggested Citation

  • Tao, Jim, 2022. "Zeta annuities, fractional calculus, and polylogarithms," MPRA Paper 112204, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:112204
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    File URL: https://mpra.ub.uni-muenchen.de/112204/1/MPRA_paper_112204.pdf
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    More about this item

    Keywords

    annuity; Riemann zeta function; fractional calculus; polylogarithm;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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