Generating functions for the Fubini type polynomials and their applications

DOI10.1007/978-3-031-46487-4_15zbMATH Open1547.11036MaRDI QIDQ6622352

Yilmaz Simsek, Neslihan Kilar

Publication date: 22 October 2024

zbMATH Keywords

Fubini-type numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Special sequences and polynomials (11B83) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

• Modification and unification of the Apostol-type numbers and polynomials and their applications
• Some array type polynomials associated with special numbers and polynomials
• Identities for Apostol-type Frobenius-Euler polynomials resulting from the study of a nonlinear operator
• Values of twisted Barnes zeta functions at negative integers
• Generating functions for \(q\)-Apostol type Frobenius-Euler numbers and polynomials
• A new generalization of the Bernoulli and related polynomials
• Special functions related to Dedekind-type DC-sums and their applications
• Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials
• Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials
• Some new families of generalized Euler and Genocchi polynomials
• Unified Apostol-Bernoulli, Euler and Genocchi polynomials
• Some new identities and congruences for Fubini numbers
• Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers
• A new approach to Euler splines
• 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 twisted \(q\)-Hurwitz zeta function and \(q\)-two-variable \(L\)-function
• \(q\)-Genocchi numbers and polynomials associated with \(q\)-Genocchi-type \(l\)-functions
• A concrete approach to classical analysis
• A family of \(p\)-adic twisted interpolation functions associated with the modified Bernoulli numbers
• Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials
• An explicit formula for the generalized Bernoulli polynomials
• New families of special numbers and polynomials arising from applications of \( p\)-adic \( q\)-integrals
• Identities associated with generalized Stirling type numbers and Eulerian type polynomials
• Generating functions for special polynomials and numbers including Apostol-type and Humbert-type polynomials
• Numerical evaluation of special power series including the numbers of Lyndon words: an approach to interpolation functions for Apostol-type numbers and polynomials
• Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
• Asymptotic expansions of the Hurwitz--Lerch zeta function
• Two variable higher-order central Fubini polynomials
• Applications of Apostol-type numbers and polynomials: approach to techniques of computation algorithms in approximation and interpolation functions
• Fubini numbers and polynomials of graphs
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• Reduction and duality of the generalized Hurwitz-Lerch zetas
• A general class of the three-variable unified Apostol-type \(q\)-polynomials and multiple power \(q\)-sums
• Generating functions for finite sums involving higher powers of binomial coefficients: analysis of hypergeometric functions including new families of polynomials and numbers
• A parametric kind of the Fubini-type polynomials
• Symmetric identities for Fubini polynomials
• A unified presentation of certain meromorphic functions related to the families of the partial zeta type functions and the \(L\)-functions
• The number of weak orderings of a finite set
• Generating function for \(q\)-Eulerian polynomials and their decomposition and applications
• Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials
• Construction of a new family of Fubini-type polynomials and its applications
• Computation methods for combinatorial sums and Euler-type numbers related to new families of numbers
• Eulerian Numbers and Polynomials
• Multiple Interpolation Functions of Higher Order (h,q)‐Bernoulli Numbers
• Central factorial numbers; their main properties and some applications.
• Preferential Arrangements
• On Some Numbers Related to the Bell Numbers
• ON q-ANALGUE OF THE TWISTED L-FUNCTIONS AND q-TWISTED BERNOULLI NUMBERS
• A NEW FAMILY OF FUBINI TYPE NUMBERS AND POLYNOMIALS ASSOCIATED WITH APOSTOL-BERNOULLI NUMBERS AND POLYNOMIALS
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• Permutations and Combination Locks
• Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications
• Formulas involving sums of powers, special numbers and polynomials arising from p-adic integrals, trigonometric and generating functions
• On central Fubini-like numbers and polynomials
• On generating functions for the special polynomials
• New families of special numbers for computing negative order Euler numbers and related numbers and polynomials
• On an open problem of Simsek concerning the computation of a family of special numbers
• Identities and relations for Fubini type numbers and polynomials via generating functions and p-adic integral approach
• A special approach to derive new formulas for some special numbers and polynomials
• Rational approximations to the zeta function
• Some Determinants Involving Incomplete Fubini Numbers
• Generating functions for two-variable polynomials related to a family of Fibonacci type polynomials and numbers
• The Factors of a Square-Free Integer
• The Number of Partitions of a Set
• A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials
• On the Factorization of Squarefree Integers
• Identities and relations for special numbers and polynomials: An approach to trigonometric functions
• Modification exponential Euler type splines derived from Apostol-Euler numbers and polynomials of complex order
• 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

This page was built for publication: Generating functions for the Fubini type polynomials and their applications