Analysis of Apostol-Type Numbers and Polynomials with Their Approximations and Asymptotic Behavior

DOI10.1007/978-3-030-60622-0_23zbMath1476.11061OpenAlexW3203572403MaRDI QIDQ5153572

Yilmaz Simsek

Publication date: 30 September 2021

Published in: Approximation Theory and Analytic Inequalities (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-60622-0_23

zbMATH Keywords

Riemann zeta functiongenerating functionsStirling numbersDirichlet characterHumbert polynomialsFrobenius-Euler polynomialsLerch zeta functionApostol-Bernoulli numbers and polynomialsApostol-Euler numbers and polynomialsDaehee numbers and polynomials\(p\)-adic \(q\)-Volkenborn integralsApostol-Changhee numbers and polynomialsBoole numbers and polynomialsPeters numbers and polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Bernoulli and Euler numbers and polynomials (11B68) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Polynomials and rational functions of one complex variable (30C10)

Related Items (3)

Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters ⋮ Applications of Apostol-type numbers and polynomials: approach to techniques of computation algorithms in approximation and interpolation functions ⋮ Some certain classes of combinatorial numbers and polynomials attached to Dirichlet characters: their construction by \(p\)-adic integration and applications to probability distribution functions

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
• Modification and unification of the Apostol-type numbers and polynomials and their applications
• Some array type polynomials associated with special numbers and polynomials
• Some identities of degenerate special polynomials
• Some new identities of Frobenius-Euler numbers and polynomials
• \(q\)-Hardy-Berndt type sums associated with \(q\)-Genocchi type zeta and \(q\)-\(l\)-functions
• A new approach to \(q\)-Genocchi numbers and their interpolation functions
• Special functions related to Dedekind-type DC-sums and their applications
• Identities involving Frobenius-Euler polynomials arising from non-linear differential equations
• Convolution identities for Cauchy numbers
• Application of a composition of generating functions for obtaining explicit formulas of polynomials
• A study on the \(p\)-adic integral representation on \(\mathbb Z_p\) associated with Bernstein and Bernoulli polynomials
• Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• \(q\)-Volkenborn integration
• On \((h,q)\)-Daehee numbers and polynomials
• A multiplication theorem for the Lerch zeta function and explicit representations of the Bernoulli and Euler polynomials
• \(q\)-Bernoulli numbers and polynomials associated with multiple \(q\)-zeta functions and basic \(L\)-series
• On the \(q\)-extension of Euler and Genocchi numbers
• On the analogs of Euler numbers and polynomials associated with \(p\)-adic \(q\)-integral on \(\mathbb Z_{p}\) at \(q= - 1\)
• Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials
• Some \(q\)-Bernoulli numbers of higher order associated with the \(p\)-adic \(q\)-integrals
• Generating functions for special polynomials and numbers including Apostol-type and Humbert-type polynomials
• \(q\)-analogue of twisted \(l\)-series and \(q\)-twisted Euler numbers
• Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
• Barnes' multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials
• Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series
• Partial derivative formulas and identities involving 2-variable Simsek polynomials
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• Generating functions for finite sums involving higher powers of binomial coefficients: analysis of hypergeometric functions including new families of polynomials and numbers
• On generating functions for Boole type polynomials and numbers of higher order and their applications
• New integral representations for Bernoulli and Euler polynomials
• Some results for the Apostol-Genocchi polynomials of higher order
• Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
• Hypergeometric summation. An algorithmic approach to summation and special function identities
• An invariant \(p\)-adic \(q\)-integral on \(\mathbb Z _p\)
• Inverse series relations and other expansions involving Humbert polynomials
• On the Lerch zeta function
• Some identities and congruences involving a certain family of numbers
• Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
• Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
• Computation methods for combinatorial sums and Euler-type numbers related to new families of numbers
• Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials
• Bernoulli polynomials of the second kind and their identities arising from umbral calculus
• ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• An Invariant P -Adic Integral Associated with Daehee Numbers
• Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications
• New families of special numbers for computing negative order Euler numbers and related numbers and polynomials
• ANALYTIC PROPERTIES OF THE q-VOLKENBORN INTEGRAL ON THE RING OF p-ADIC INTEGERS
• Functional Equations associated with Generalized Bernoulli Numbers and Polynomials
• A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials
• Some new identities and formulas for higher-order combinatorial-type numbers and polynomials
• On Boole-type combinatorial numbers and polynomials

This page was built for publication: Analysis of Apostol-Type Numbers and Polynomials with Their Approximations and Asymptotic Behavior