相关论文: Reflection identities of harmonic sums up to weigh…
We consider the reflection identities for harmonic sums at weight four. We decompose a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or positive values of the…
We analyze the structure of the eigenvalue of the color-singlet Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation in N=4 SYM in terms of the meromorphic functions obtained by the analytic continuation of harmonic sums from positive even integer…
We analyze known results of next-to-next-to-leading(NNLO) singlet BFKL eigenvalue in $N=4$ SYM written in terms of harmonic sums. The nested harmonic sums building known NNLO BFKL eigenvalue for specific values of the conformal spin have…
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.
Two types of finite series of products of harmonic numbers involving nonnegative integer powers are evaluated, also yielding two other important harmonic number identities. The recursion formulas for these sums are derived, which are easily…
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.
In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can be derived involve products of binomial coefficients and…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
We consider the powers of leading order eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation at zero conformal spin. Using reflection identities of harmonic sums we demonstrate how involved generalized polygamma functions are…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
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…
Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first…
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
In this work we prove a new combinatorial identity and applying it we establish many finite harmonic sum identities. Among many others, we prove that \begin{equation*}…
For any $m,n\in\mathbb{N}$ we first give new proofs for the following well known combinatorial identities \begin{equation*} S_n(m)=\sum\limits_{k=1}^n\binom{n}{k}\frac{(-1)^{k-1}}{k^m}=\sum\limits_{n\geq r_1\geq r_2\geq...\geq r_m\geq…
We analyze the known results for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in the perturbative regime using the analytic continuation of harmonic sums from even positive arguments to the complex plane. The…
We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic…
We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form. These relations depend on the structure of the index…