New Multiple Harmonic Sum Identities
نویسندگان
چکیده
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.
منابع مشابه
New Harmonic Number Identities with Applications
We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums ∑n k=1 ∏r j=1Hk({1} ) when ∑r j=1 λj ≤ 5. We apply these identities to the study of two congruences modulo a power of a prime.
متن کاملar X iv : m at h / 00 10 14 0 v 1 [ m at h . Q A ] 1 3 O ct 2 00 0 RELATIONS OF MULTIPLE ZETA VALUES AND THEIR ALGEBRAIC EXPRESSION
We establish a new class of relations among the multiple zeta values ζ(k1, . . . , kl) = ∑ n1>···>nl≥1 1 n k1 1 · · ·n kl k , which we call the cyclic sum identities. These identities have an elementary proof, and imply the “sum theorem” for multiple zeta values. They also have a succinct statement in terms of “cyclic derivations” as introduced by Rota, Sagan and Stein. In addition, we discuss ...
متن کاملBinomial Coefficient–harmonic Sum Identities Associated to Supercongruences
We establish two binomial coefficient–generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of the author, they are used to establish modulo p (k > 1) congruences between truncated generalized hypergeometric series, and a function which extends Greene’s ...
متن کاملMultiple q-zeta values
We introduce a q-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple q-zeta values satisfy a q-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values. Additionally, multiple q-zeta values can be viewed as special values of the multiple q-polylogarithm, which ad...
متن کامل6 F eb 2 00 4 MULTIPLE q - ZETA VALUES
We introduce a q-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple q-zeta values satisfy a q-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values. Additionally, multiple q-zeta values can be viewed as special values of the multiple q-polylogarithm, which ad...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 21 شماره
صفحات -
تاریخ انتشار 2014