Sum of interpolated finite multiple harmonic q-series
نویسندگان
چکیده
منابع مشابه
Duality for finite multiple harmonic q-series
7 We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums 9 involving the Gaussian binomial coefficients. Special cases of these identities—for example, with all parameters equal to 1—have occurred in the literature. The special case with only one pa...
متن کاملTWO IDENTITIES FOR MULTIPLE HARMONIC q-SERIES
Abstract. We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial coefficients. Special cases of these identities—for example, with all parameters equal to 1—have occurred in the literature. The special case with only ...
متن کاملThe Algebra of a q-Analogue of Multiple Harmonic Series
We introduce an algebra which describes the multiplication structure of a family of q-series containing a q-analogue of multiple zeta values. The double shuffle relations are formulated in our framework. They contain a q-analogue of Hoffman’s identity for multiple zeta values. We also discuss the dimension of the space spanned by the linear relations realized in our algebra.
متن کاملNew Multiple Harmonic Sum Identities
We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.
متن کاملSUM OF MULTIPLE q-ZETA VALUES
The generating function of the sums of multiple q-zeta values with fixed weights, depths and 1-heights, 2-heights, . . . , r-heights is represented in terms of specializations of basic hypergeometric functions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2019.02.024