Extensions of the Genocchi polynomials and their Fourier expansions and integral representations

Publication date: 10 February 2012

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1315318341

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Other functions defined by series and integrals (33E20) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (48)

Fourier expansion and integral representation generalized Apostol-type Frobenius-Euler polynomials ⋮ A new generalization of Apostol-type Laguerre-Genocchi polynomials ⋮ Some new formulas for the products of the Apostol type polynomials ⋮ A new unified family of generalized Apostol-Euler, Bernoulli and Genocchi polynomials ⋮ Two closed forms for the Apostol-Bernoulli polynomials ⋮ Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials ⋮ Evaluation of Apostol-Euler based poly Daehee polynomials ⋮ Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi poly\-nomials ⋮ Construction of a new family of Fubini-type polynomials and its applications ⋮ Confluent Appell polynomials ⋮ An extension of generalized Apostol-Euler polynomials ⋮ Unified Bernstein and Bleimann-Butzer-Hahn basis and its properties ⋮ Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials ⋮ Integral modification of beta-Apostol-Genocchi operators ⋮ Derivation of identities involving some special polynomials and numbers via generating functions with applications ⋮ Some series identities involving the generalized Apostol type and related polynomials ⋮ A family of Apostol-Euler polynomials associated with Bell polynomials ⋮ Unnamed Item ⋮ Asymptotics of Genocchi polynomials and higher order Genocchi polynomials using residues ⋮ A new class of generalized Apostol-Bernoulli polynomials and some analogues of the Srivastava-Pintér addition theorem ⋮ Generalized Hermite- based Apostol- Bernoulli, Euler, Genocchi polynomials and their relations ⋮ Fourier series of sums of products of Genocchi functions and their applications ⋮ About extensions of generalized Apostol-type polynomials ⋮ A new formula of products of the Apostol-Bernoulli and Apostol-Euler polynomials ⋮ Some results for Apostol-type polynomials associated with umbral algebra ⋮ Finding symmetry identities for the 2-variable Apostol type polynomials ⋮ A set of finite order differential equations for the Appell polynomials ⋮ Some new generalizations and applications of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials ⋮ Certain results for the 2-variable Apostol type and related polynomials ⋮ Certain new presentation of the generalized polynomials and numbers ⋮ Some unified formulas and representations for the Apostol-type polynomials ⋮ A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra ⋮ A new class of Laguerre-based Apostol type polynomials ⋮ Approximation by a new sequence of operators involving Apostol-Genocchi polynomials ⋮ Certain generating funtion of generalized Apostol type Legendre-based polynomials ⋮ Series representations at special values of generalized Hurwitz-Lerch zeta function ⋮ 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 ⋮ Approximations of Genocchi polynomials of complex order ⋮ A parametric kind of the Fubini-type polynomials ⋮ Higher-order convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials ⋮ A note on the truncated-exponential based Apostol-type polynomials ⋮ A Riordan array approach to Apostol type-Sheffer sequences ⋮ Durrmeyer variant of Apostol-Genocchi-Baskakov operators ⋮ Fourier expansions for higher-order Apostol-Genocchi, Apostol-Bernoulli and Apostol-Euler polynomials ⋮ The multi-variable unified family of generalized Apostol-type polynomials ⋮ Sine and cosine types of generating functions ⋮ Certain Laguerre-based Generalized Apostol Type Polynomials

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