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On q-poly-Bernoulli numbers arising from combinatorial interpretations
In this paper we present several natural q -analogues of the poly-Bernoulli numbers arising in combinatorial contexts. We also recall some related...
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Applications of Apostol-type Numbers and Polynomials: Approach to Techniques of Computation Algorithms in Approximation and Interpolation Functions
The purpose of this chapter is to survey and make a compilation that covers many families of the special numbers and polynomials including the...
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λ-Analogues of Stirling polynomials of the first kind and their applications
Recently, λ -analogues of Stirling numbers of the first kind were studied. In this paper, we introduce, as natural extensions of these numbers, λ -Stirl...
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The r-central factorial numbers with even indices
In this paper, we introduce the r -central factorial numbers with even indices of the first and second kind as extended versions of the central...
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Special Numbers
Fibonacci, son of Bonaccio, was the Italian mathematician Leonardo of Pisa who lived in the twelfth and thirteenth centuries.
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Two problems of binomial sums involving harmonic numbers
Two open problems recently proposed by ** and Luo (Adv. Differ. Equ. 2021:38,
2021 ) are resolved by evaluating explicitly three binomial sums... -
Boole-Dunkl polynomials and generalizations
Appell sequences of polynomials can be extended to the Dunkl context replacing the ordinary derivative by the Dunkl operator on the real line, and...
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Partial-fraction decomposition of a rational function and its application
In this paper, by using the residue method of complex analysis, we obtain an explicit partial fraction decomposition for the general rational...
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Analysis of Apostol-Type Numbers and Polynomials with Their Approximations and Asymptotic Behavior
In this chapter, using the methods and techniques of approximation of some classical polynomials and numbers including the Apostol–Bernoulli numbers...
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Summation formulas of q-hyperharmonic numbers
In this paper, several weighted summation formulas of q -hyperharmonic numbers are derived. As special cases, several formulas of hyperharmonic...
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Generalized hypergeometric Bernoulli numbers
We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. We study their properties, including relations, expressions and...
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Apostol type (p, q)-Frobenius–Eulerian polynomials and numbers
The main purpose of this paper is to introduce Apostol type ( p , q )-Frobenius–Eulerian numbers and polynomials and investigate some of their basic...
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Degenerate poly-Bell polynomials and numbers
Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi...
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On Some Sequences of Polynomials Generating the Genocchi Numbers
We consider sequences of Genocchi numbers of the first and the second kind. For these numbers, an approach based on their representation using...
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New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums
By applying p -adic integral, in Simsek (Montes Taurus J Pure Appl Math 3(1):38–61, 2021), we constructed generating function for the special numbers...
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Multiple Convolution Formulae of Bernoulli and Euler Numbers
By examining higher derivatives of hyperbolic functions, we derive monomial and binomial representation formulae, that are utilized to establish...