Explicit Evaluation of Some Quadratic Euler-Type Sums Containing Double-Index Harmonic Numbers

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Explicit evaluation of Euler sums

In response to a letter from Goldbach, Euler considered sums of the form where s and t are positive integers. As Euler discovered by a process of extrapolation (from s + t 13), h (s; t) can be evaluated in terms of Riemann-functions when s + t is odd. We provide a rigorous proof of Euler's discovery and then give analogous evaluations with proofs for corresponding alternating sums. Relatedly we...

متن کامل

Explicit evaluation of some exponential sums

Let m be a positive integer, let r be a prime such that 2 is a primitive root modulo r, and let q = 2(r−1)r m−1 . In this note a binomial exponential sum over Fq which assumes 3 2 log2 q + 2 distinct values is explicitly evaluated and its value distribution is determined.

متن کامل

Real Quadratic Double Sums

In 1988, Andrews, Dyson and Hickerson initiated the study of q-hypergeometric series whose coefficients are dictated by the arithmetic in real quadratic fields. In this paper, we provide a dozen q-hypergeometric double sums which are generating functions for the number of ideals of a given norm in rings of integers of real quadratic fields and prove some related identities.

متن کامل

On Stirling Numbers and Euler Sums

In this paper, we propose the another yet generalization of Stirling numbers of the rst kind for non-integer values of their arguments. We discuss the analytic representations of Stirling numbers through harmonic numbers, the generalized hypergeometric function and the logarithmic beta integral. We present then in nite series involving Stirling numbers and demonstrate how they are related to Eu...

متن کامل

Evaluation of Euler-zagier Sums

We present a simple method for evaluation of multiple Euler sums in terms of single and double zeta values. 2000 Mathematics Subject Classification. 11M99, 40B05.

متن کامل

ذخیره 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: Tatra Mountains Mathematical Publications

سال: 2020

ISSN: 1210-3195

DOI: 10.2478/tmmp-2020-0034