Apéry-type(inverse)binomial series have appeared prominently in the calculations of Feynman integrals in recent years.In their previous work,the authors showed that a few large classes of the non-alternating Ape...Apéry-type(inverse)binomial series have appeared prominently in the calculations of Feynman integrals in recent years.In their previous work,the authors showed that a few large classes of the non-alternating Ape′ry-type(inverse)central binomial series can be evaluated using colored multiple zeta values of level four(i.e.,special values of multiple polylogarithms at the fourth roots of unity)by expressing them in terms of iterated integrals.In this sequel,the authors will prove that for several classes of the alternating versions they need to raise the level to eight.Their main idea is to adopt hyperbolic trigonometric 1-forms to replace the ordinary trigonometric ones used in the non-alternating setting.展开更多
基金supported by the National Natural Science Foundation of China(No.12101008)the Natural Science Foundation of Anhui Province(No.2108085QA01)the Jacobs Prize from the Bishop’s School。
文摘Apéry-type(inverse)binomial series have appeared prominently in the calculations of Feynman integrals in recent years.In their previous work,the authors showed that a few large classes of the non-alternating Ape′ry-type(inverse)central binomial series can be evaluated using colored multiple zeta values of level four(i.e.,special values of multiple polylogarithms at the fourth roots of unity)by expressing them in terms of iterated integrals.In this sequel,the authors will prove that for several classes of the alternating versions they need to raise the level to eight.Their main idea is to adopt hyperbolic trigonometric 1-forms to replace the ordinary trigonometric ones used in the non-alternating setting.
