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| Alternating Ap´ery-Type Series and Colored Multiple Zeta Values of Level Eight |
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Citation： |
Ce XU,Jianqiang ZHAO.Alternating Ap´ery-Type Series and Colored Multiple Zeta Values of Level Eight[J].Chinese Annals of Mathematics B,2025,46(4):559~582 |
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Net amount： 7 |
Authors： |
Ce XU; Jianqiang ZHAO |
Foundation： |
the National Natural Science Foundation of China (No. 12101008); the Natural Science Foundation of Anhui Province (No. 2108085QA01) and the Jacobs Prize from the Bishop’s School. |
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| Abstract： |
Ap′ery-type (inverse) binomial series have appeared prominently in the calculations of Feynman integrals in recent years. In their previous work; the authors showedthat a few large classes of the non-alternating Ap′ery-type (inverse) central binomial series can be evaluated using colored multiple zeta values of level four (i.e.; special valuesof multiple polylogarithms at the fourth roots of unity) by expressing them in terms ofiterated integrals. In this sequel; the authors will prove that for several classes of thealternating versions they need to raise the level to eight. Their main idea is to adopthyperbolic trigonometric 1-forms to replace the ordinary trigonometric ones used in thenon-alternating setting. |
Keywords： |
Ap´ery-type series Colored multiple zeta values Binomial coefficients Iterated integrals |
Classification： |
Ap′ery-type series; Colored multiple zeta values; Binomial coefficients;
Iterated integrals |
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