Related papers: Summation formulas involving generalized harmonic …
In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series…
Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking…
We give a definition of generalized hypergeometric functions over finite fields using modified Gauss sums, which enables us to find clear analogy with classical hypergeometric functions over the complex numbers. We study their fundamental…
Gencev has recently reported a closed form summation for an infinite series involving the harmonic numbers and the central binomial numbers. This note indicates a possible approach to the proof involving the dilogarithm function.
The asymptotic behaviour of partial sums of generalized hypergeometric series of unit argument is investigated.
Using generalized hypergeometric functions to perform symbolic manipulation of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other…
The duality is a fundamental property of the finite multiple harmonic sums (MHS). In this paper, we prove a duality result for certain generalizations of MHS which appear naturally as the differences of MHS. We also prove a formula for the…
We show various supercongruences for truncated series which involve central binomial coefficients and harmonic numbers. The corresponding infinite series are also evaluated.
We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also…
Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument, when one numerator parameter and one denominator parameter are negative integers. Further,…
We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{\lambda_j})$ when $\sum_{j=1}^r \lambda_j\leq 5$. We apply these identities to the study of two…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…
In this paper, we provide a general framework for obtaining the formula for nested summation of powers of natural numbers. We define a special triangular array of numbers from which we can obtain the formula for nested summation of natural…
Based on some combinatorial identities arising from symbolic summation, we extend two supercongruences on partial sums of hypergeometric series, which were originally conjectured by Guo and Schlosser and recently confirmed by Jana and…
We demonstrate that certain classes of Schl\" omilch-like infinite series and series that include generalized hypergeometric functions can be calculated in closed form starting from a simple quantum model of a particle trapped inside an…