Truncated Hypergeometric Functions and Discretized Integrals

Abstract

We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between truncated series and discretized integrals which comes from the mutliple zeta values and multiple polylogarithms. We also prove the formula of Ohno-Zagier type which relates the truncated multiple polylogarithms and the truncated hypergeometric series.

21 pages; Remark 5.6 (2) is inserted; Section 6 is added