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Infinite Summation Formulas for Triple Lauricella Hypergeometric Functions
Inspired by the work by Brychkov and Saad who gave infinite summation formulas for Appell functions (of two variables) with the help of summation...
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Functional Summation of Series
AbstractWe consider a summation technique which reduces summation of a series to the solution of some linear functional equations. Partial sums of a...
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Precision-aware deterministic and probabilistic error bounds for floating point summation
We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions...
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Some Terminating K-Balanced Clausen Hypergeometric Summation Theorems
The main aim of this paper is to establish some new hypergeometric summation theorems (
14 ), (34 ) and the results (41 ), (42 ), (43 ) and (44 ) (not... -
Generalized Glaisher-Kinkelin constants and Ramanujan summation of series
We study a sequence of constants known as the Bendersky-Adamchik constants which appear quite naturally in number theory and generalize the classical...
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A Voronoi summation formula for the shifted triple divisor function
In this paper, we prove a Voronoi summation formula for the shifted threefold divisor function twisted by additive characters. As the main tool, we...
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Tree Summation Formulas
It is a common feature in mathematics that recursive formulas can often be expanded into summation formulas over a certain set of combinatorial data....
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Some Congruences from the Karlsson-Minton Summation Formula
Let p be an odd prime. In this paper, by using the well-known Karlsson-Minton summation formula, we mainly prove two supercongruences as variants of...
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Summation and Integration
Informally, indefinite integration refers to the problem of finding an antiderivative for a given function, i.e., given f, the task is to find g such...
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Summation Made Easy
A magicians’ congress will soon be held in Right Angleton, where magicians from all over the world will perform their magic tricks in various...
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Applications of the Lipschitz Summation Formula and a Generalization of Raabe’s Cosine Transform
General summation formulas have been proved to be very useful in analysis, number theory and other branches of mathematics. The Lipschitz summation...
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On a Method for Uniform Summation of the Fourier-Jacobi Series
The paper deals with the study of a matrix method of summation which is stronger than all the Cesàro summation methods and which assures the uniform...
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Energy-Stable Global Radial Basis Function Methods on Summation-By-Parts Form
Radial basis function methods are powerful tools in numerical analysis and have demonstrated good properties in many different simulations. However,...
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On Approximate Summation of Poincaré Series in the Schottky Model
AbstractFor approximate summation of Poincaré theta series in the Schottky model of real hyperelliptic curves, modifications of the Bogatyrev and...
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Summation of Poincaré Theta Series in the Schottky Model
AbstractNew algorithms for approximate summation of Poincaré theta series in the Schottky model of real hyperelliptic curves are proposed. As a...
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Rational Solutions to the KPI Equation as Multi-lumps with a One Degree of Summation
In this paper, we construct solutions to the Kadomtsev–Petviashvili equation (KPI) by using a Darboux transformation with particular genera-ting...
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A Summation Method for Trigonometric Fourier Series Based on Sinc-Approximations
We propose a summation method for trigonometric Fourier series. We use the sequential approach for defining generalized functions. The method makes...
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On an Eigenvalue Property of Summation-By-Parts Operators
Summation-By-Parts (SBP) methods provide a systematic way of constructing provably stable numerical schemes. However, many proofs of convergence and...