Explicit Formulas Associated with Some Families of Generalized Bernoulli and Euler Polynomials
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DOI: 10.1007/s00009-017-0891-0
Abstract: In this paper, we propose and derive several new explicit formulas of the generalized Bernoulli and Euler polynomials in terms of the generalized Stirling numbers of the second kind. A study of some families of… read more here.
Keywords: associated families; bernoulli euler; formulas associated; euler polynomials ... See more keywords
A (p, q)-Analog of Poly-Euler Polynomials and Some Related Polynomials
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DOI: 10.1007/s11253-020-01799-6
Abstract: UDC 517.5 We introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give several combinatorial identities and properties… read more here.
Keywords: analog poly; poly euler; euler polynomials; polynomials related ... See more keywords
Construction on the Degenerate Poly-Frobenius-Euler Polynomials of Complex Variable
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DOI: 10.1155/2021/3115424
Abstract: In this paper, we introduce degenerate poly-Frobenius-Euler polynomials and derive some identities of these polynomials. We give some relationships between degenerate poly-Frobenius-Euler polynomials and degenerate Whitney numbers and Stirling numbers of the first kind. Moreover,… read more here.
Keywords: euler polynomials; poly frobenius; degenerate poly; frobenius euler ... See more keywords
Quadratic symmetry of modified q-Euler polynomials
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DOI: 10.1186/s13662-018-1493-2
Abstract: We use the p-adic q-integral and group action to count the number of the generating functions of modified q-Euler polynomials in a prescribed set. Some generating function yields modified q-Euler polynomials with the isotropy group… read more here.
Keywords: modified euler; group; euler polynomials; quadratic symmetry ... See more keywords
Construction of Fourier expansion of Apostol Frobenius–Euler polynomials and its applications
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DOI: 10.1186/s13662-018-1526-x
Abstract: In the present paper, we find the Fourier expansion of the Apostol Frobenius–Euler polynomials. By using a Fourier expansion of the Apostol Frobenius–Euler polynomials, we derive some new and interesting results. read more here.
Keywords: apostol frobenius; expansion apostol; euler polynomials; fourier expansion ... See more keywords
Truncated-exponential-based Frobenius–Euler polynomials
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DOI: 10.1186/s13662-019-2462-0
Abstract: In this paper, we first introduce a new family of polynomials, which are called the truncated-exponential based Frobenius–Euler polynomials, based upon an exponential generating function. By making use of this exponential generating function, we obtain… read more here.
Keywords: truncated exponential; exponential based; frobenius euler; euler polynomials ... See more keywords
Truncated euler polynomials
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DOI: 10.1515/ms-2017-0122
Abstract: Abstract We define a truncated Euler polynomial Em,n(x) as a generalization of the classical Euler polynomial En(x). In this paper we give its some properties and relations with the hypergeometric Bernoulli polynomial. read more here.
Keywords: euler; truncated euler; euler polynomials;
On the generalized q-poly-Euler polynomials of the second kind
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DOI: 10.2298/fil2002475k
Abstract: In this work, we define the generalized q-poly-Euler numbers of the second kind of order ? and the generalized q-poly-Euler polynomials of the second kind of order ?. We investigate some basic properties for these… read more here.
Keywords: second kind; kind; euler polynomials; poly euler ... See more keywords
Some recurrence formulas for the q-Bernoulli and q-Euler polynomials
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DOI: 10.2298/fil2002663d
Abstract: The recurrence relations have a very important place for the special polynomials such as q-Appell polynomials. In this paper, we give some recurrence formulas that allow us a better understanding of q-Appell polynomials. We investigate… read more here.
Keywords: recurrence formulas; bernoulli euler; euler polynomials; formulas bernoulli ... See more keywords
New Formulas and Connections Involving Euler Polynomials
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DOI: 10.3390/axioms11120743
Abstract: The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as… read more here.
Keywords: formulas connections; euler polynomials; polynomials new; new formulas ... See more keywords
Explicit Properties of Apostol-Type Frobenius–Euler Polynomials Involving q-Trigonometric Functions with Applications in Computer Modeling
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DOI: 10.3390/math11102386
Abstract: In this article, we define q-cosine and q-sine Apostol-type Frobenius–Euler polynomials and derive interesting relations. We also obtain new properties by making use of power series expansions of q-trigonometric functions, properties of q-exponential functions, and… read more here.
Keywords: trigonometric functions; apostol type; euler polynomials; frobenius euler ... See more keywords