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Euler sums of multiple hyperharmonic numbers
For k ≔ ( k 1 , …, k r ) ∈ ℕ r and n , m ∈ ℕ, we extend the definition of classical hyperharmonic numbers to define the multiple hyperharmonic numbers
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On two supercongruences involving Almkvist-Zudilin sequences
We prove two supercongruences involving Almkvist-Zudilin sequences, which were originally conjectured by Z.-H. Sun (2020).
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An Algebraic Approach to Degenerate Appell Polynomials and Their Hybrid Forms via Determinants
It is remarkable that studying degenerate versions of polynomials from algebraic point of view is not limited to only special polynomials but can...
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Asymptotics of Generalized Partial Theta Functions with a Dirichlet Character
We prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain L -series....
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Character Gamma Functions and Evaluation of Series with Dirichlet L-Value Coefficients
In this paper, we demonstrate a character analogue of the Lerch formula and multiplication formulas for the Dirichlet L -functions. These formulas...
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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...
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Congruences for certain families of Apéry-like sequences
We systematically investigate the expressions and congruences for both a one-parameter family { G n ( x )} as well as a two-parameter family { G n ( r, m )} of...
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Reciprocity formulas for Hall–Wilson–Zagier type Hardy–Berndt sums
We introduce vast generalizations of the Hardy–Berndt sums. They involve higher-order Euler and/or Bernoulli functions, in which the variables are...
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Several Expressions of Dirichlet L-function at Positive Integers
In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we...
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On (p, q)-Appell Polynomials
We introduce polynomial sets of ( p , q )-Appell type and give some characterizations of them. The algebraic properties of the set of all polynomial...
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Poly-
p -Bernoulli polynomials and generalized Arakawa–Kaneko zeta functionIn this paper, we first obtain several properties of poly- p -Bernoulli polynomials. In particular, we achieve some new results for poly-Bernoulli...
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A New Type of Euler Polynomials and Numbers
By defining two specific exponential generating functions, we introduce a kind of Euler polynomials and study its basic properties in detail. As an...
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Ramanujan’s Harmonic Number Expansion and Two Identities for Bernoulli Numbers
By the Lagrange–Bürmann formula, we provide a new explicit formula for determining the coefficients of Ramanujan’s asymptotic expansion for the n th...
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On hypergeometric Bernoulli numbers and polynomials
We provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and...
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Generalized poly-Cauchy and poly-Bernoulli numbers by using incomplete \({\varvec{r}}\)-Stirling numbers
In this paper we introduce restricted r -Stirling numbers of the first kind. Together with restricted r -Stirling numbers of the second kind and the...
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Explicit Formulas Associated with Some Families of Generalized Bernoulli and Euler Polynomials
In this paper, we propose and derive several new explicit formulas of the generalized Bernoulli and Euler polynomials in terms of the generalized...
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Explicit Formulas for Special Values of the Bell Polynomials of the Second Kind and for the Euler Numbers and Polynomials
In the paper, the authors establish by two approaches several explicit formulas for special values of the Bell polynomials of the second kind, derive...
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Sum Relations of Multiple Zeta Star Values with Even Arguments
The purpose of this paper is the presentation of an identity which is closely related to the sum relation involving multiple zeta star values with...
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Incomplete Poly-Bernoulli Numbers and Incomplete Poly-Cauchy Numbers Associated to the q-Hurwitz–Lerch Zeta Function
In this paper we introduce a q -analogue of the incomplete poly-Bernoulli numbers and incomplete poly-Cauchy numbers by using the q -Hurwitz–Lerch zeta...