Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas

DOI10.1007/978-3-030-37904-9_10OpenAlexW3010696385MaRDI QIDQ3296685

Gradimir V. Milovanović, Yilmaz Simsek

Publication date: 1 July 2020

Published in: Trigonometric Sums and Their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-37904-9_10

zbMATH Keywords

Eisenstein seriesDedekind sumsdegree of exactnesstrigonometric sumsHardy sumsGauss-Chebyshev quadrature sums

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical analysis (65-XX) Approximations and expansions (41Axx) General and miscellaneous specific topics (00Axx) Tables in numerical analysis (65Axx)

Related Items (5)

Further developments of basic trigonometric power sums ⋮ Poly-Dedekind sums associated with poly-Bernoulli functions ⋮ Some identities and reciprocity relations of unipoly-Dedekind type DC sums ⋮ Applications of Apostol-type numbers and polynomials: approach to techniques of computation algorithms in approximation and interpolation functions ⋮ On an approach for evaluating certain trigonometric character sums using the discrete time heat kernel

Uses Software

• OPQ

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dedekind sums involving Jacobi modular forms and special values of Barnes zeta functions
• Special functions related to Dedekind-type DC-sums and their applications
• Basic trigonometric power sums with applications
• Summation formulae for finite tangent and secant sums
• Some expansions in basic Fourier series and related topics
• Summation formulae for finite cotangent sums
• Cotangent sums, a further generlization of Dedekind sums
• Gauss-Radau and Gauss-Lobatto quadratures with double end points
• Integral representations of the Legendre chi function
• On the remainder term of Gauss-Radau quadratures for analytic functions
• Euler numbers and polynomials associated with zeta functions
• Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
• On analytic properties and character analogs of Hardy sums
• Dedekindsummen mit elliptischen Funktionen
• On the remainder term for analytic functions of Gauss-Lobatto and Gauss- Radau quadratures
• Reciprocity theorems for Dedekind sums and generalizations
• On Turán quadrature formulas for the Chebyshev weight
• Derivative polynomials, Euler polynomials, and associated integer sequences
• On Gaussian quadrature formulas for the Chebyshev weight
• \(S\)-orthogonality and construction of Gauss-Turán-type quadrature formulae
• On some trigonometric power sums
• Reciprocal relations for trigonometric sums
• Remarks on some relationships between the Bernoulli and Euler polynomials.
• Explicit evaluations and reciprocity theorems for finite trigonometric sums
• Relations between theta-functions, Hardy sums, Eisenstein and Lambert series in the transformation formula of log \(\eta_{g,h}(z)\).
• \(q\)-Dedekind type sums related to \(q\)-zeta function and basic \(L\)-series
• The error norm of Gauss-Radau quadrature formulae for Chebyshev weight functions
• Summation of a family of finite secant sums
• Trigonometric orthogonal systems and quadrature formulae
• Quadrature formulae
• Higher dimensional Dedekind sums
• The remainder term for analytic functions of Gauss-Radau and Gauss- Lobatto quadrature rules with multiple end points
• Generalized Dedekind sums and transformation formulae of certain Lambert series
• On the Lerch zeta function
• Theorems on generalized Dedekind sums
• Some theorems on generalized Dedekind sums
• Trigonometric Representations of Generalized Dedekind and Hardy Sums via the Discrete Fourier Transform
• Analytic Number Theory, Approximation Theory, and Special Functions
• Closed-form summations of Dowker's and related trigonometric sums
• Analytic Properties of Arithmetic Sums Arising in the Theory of the Classical Theta-Functions
• SOME IDENTITIES INVOLVING THE LEGENDRE'S CHI-FUNCTION
• Interpolation Processes
• Note on the Euler Numbers and Polynomials
• ON ELLIPTIC ANALOGUE OF THE HARDY SUMS
• Dedekind and Hardy sums
• On Verlinde's formula for the dimensions of vector bundles on moduli spaces
• Dedekind Sums and a Paper of G. H. Hardy
• Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
• Values of the Legendre chi and Hurwitz zeta functions at rational arguments
• Zur Theorie der Modulfunktionen.
• Dedekind cotangent sums
• Reciprocity formulae for general Dedekind-Rademacher sums
• Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part II
• Generalized cosecant numbers and trigonometric inverse power sums
• On a finite sum with powers of cosines
• Note on on Dedekind type DC sums
• Quadrature Rules with Multiple Nodes
• Secant and cosecant sums and Bernoulli-Nörlund polynomials
• A generalization of the Hurwitz - Lerch Zeta function
• Dedekind-Rademacher Sums
• Dedekind-Rademacher sums and their reciprocity formula.
• Analytic Continuation of the Series ∑(m + nz) -s
• Analytic Continuation of Eisenstein Series
• Generalized Dedekind Eta-Functions and Generalized Dedekind Sums
• On Generalized Hardy Sums s 5(h, k)
• On the Hurwitz zeta-function
• Sommes de Dedekind elliptiques et formes de Jacobi. (Elliptic Dedekind sums and Jacobi forms).
• Quadratures with multiple nodes, power orthogonality, and moment-preserving spline approximation
• The remainder term for analytic functions of Gauss-Lobatto quadratures

This page was built for publication: Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas