We introduce the multivariable connected sum which is a generalization of Seki–Yamamoto’s connected sum and prove the fundamental identity for these sums by series manipulation. This identity yields explicit procedures for evaluating multivariable connected sums and for giving relations among special values of multiple polylogarithms. In particular, our class of relations contains Ohno’s relations for multiple polylogarithms.

We prove some weighted sum formulas for half multiple zeta values, half finite multiple zeta values, and half symmetric multiple zeta values. The key point of our proof is Dougall's identity for the generalized hypergeometric function 5F4. Similar results for interpolated refined symmetric multiple zeta values and half refined symmetric multiple zeta values are also discussed.

In this paper, we introduce the hypermultiple gamma functions of BM-type and prove the asymptotic expansion of these functions.

The multiple gamma functions of BM (Barnes-Milnor) type and the q-multiple gamma functions have been studied independently. In this paper, we introduce a new generalization of the multiple gamma functions called the q-BM multiple gamma function including those functions and prove some properties the BM multiple gamma functions satisfy for them.