Related papers: A note on a generalized circular summation formula…
Euler's transformation formula for the Gauss hypergeometric function 2F1 is extended to hypergeometric functions of higher order. Unusually, the generalized transformation constrains the hypergeometric function parameters algebraically but…
Mimicking the idea of the generalized Hamming weight of linear codes, we introduce a new lattice invariant, the generalized theta series. Applications range from identifying stable lattices to the lattice isomorphism problem. Moreover, we…
We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group. We show that…
We offer some summation formulas that appear to have great utility in probability theory. The proofs require some recent results from analysis that have thus far been applied to basic hypergeometric functions.
Introducing a notion of the weighted mean sigma-r curvature and using the weighted Newton transformations we derive in this paper some integral formulae on weighted manifolds. These formulae generalize the flux formula and some of its…
In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].
In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and…
We determine the three-loop $\overline{\text{MS}}$ quartic $ \beta $-function for the most general renormalisable four-dimensional theories. A general parametrization of the $ \beta $-function is compared to known $ \beta $-functions for…
In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.
The purpose of this article is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.
We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions.
Continuing previous work, this paper focuses on the summability problem of multivariate rational functions in the mixed case in which both shift and $q$-shift operators can appear. Our summability criteria rely on three ingredients…
In this paper, we consider a discrete version of iterated integrals by the naive (equally divided) Riemann sum. In particular, basic three formulas for usual iterated integrals are discritized. Moreover, we proved cyclic sum formulas for…
Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at $p$ equally shifted points were recently found. The purpose of this paper is to re-express these cyclic identities in terms of ratios of Jacobi…
The Watson-Harkins sum involving the product of the cosine and cosecant functions is extended to derive the finite sum of generalized Hurwitz-Lerch Zeta functions is derived in terms of the Hurwitz-Lerch Zeta function. A transformation…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications follow. Related compatibility questions for…
\begin{abstract} We apply the theory of generalized Watson transforms developed in \cite{zheng00} to construct the complementary series of $GL(2,\R)$. \end{abstract}
Generalization of the integral representation of the gamma function has been obtained, which shows that the Hankel contour assumes rotation in the complex plane. The range of admissible values for the contour rotation angle is set. Using…