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.
| Item Type: | MPRA Paper |
|---|---|
| Original Title: | Zeta annuities, fractional calculus, and polylogarithms |
| Language: | English |
| Keywords: | annuity, Riemann zeta function, fractional calculus, polylogarithm |
| Subjects: | G - Financial Economics > G2 - Financial Institutions and Services > G22 - Insurance ; Insurance Companies ; Actuarial Studies |
| Item ID: | 112204 |
| Depositing User: | Dr. Jim Tao |
| Date Deposited: | 08 Mar 2022 08:33 |
| Last Modified: | 08 Mar 2022 08:33 |
| References: | [1] Leslie Jane Federer Vaaler and James W. Daniel. Mathematical interest theory. Mathematical Association of America, Washington, DC, second edition, 2009. [2] Roudy El Haddad. Repeated Integration and Explicit Formula for the nth Integral of xm(ln x)m′. arXiv e-prints, page arXiv:2102.11723, February 2021. [3] Leonard Lewin, editor. Structural properties of polylogarithms, volume 37 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1991. |
| URI: | https://mpra.ub.uni-muenchen.de/id/eprint/112204 |
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