A NEW TYPE OF DEGENERATE POLY-TYPE 2 EULER POLYNOMIALS AND DEGENERATE UNIPOLY-TYPE 2 EULER POLYNOMIALS
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초록
The polylogarithm function was introduced by Kim-Kim (Russ. J. Math. Phys. 27(2), 227-235(2020)). In addition, many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is the degenerate poly-type 2 Euler polynomials and numbers. This focus stems from their importance for applications in combinatorics, number theory and in other aspects of applied mathematics. we construct a new type of degenerate poly-type 2 Euler polynomials by using the degenerate polylogarithm function, called degenerate poly-type 2 Euler polynomials and numbers. We also show several combinatorial identities related to the degenerate poly-type 2 Euler polynomials and numbers. We also construct the degenerate unipolytype 2 Euler polynomials attached to an arithmetic function. By using the degenerate polylogarithm function, we also give some new explicit expressions and identities related to degenerate unipoly-type 2 Euler polynomials and some special numbers and polynomials.
Abstract
The polylogarithm function was introduced by Kim-Kim (Russ. J. Math. Phys. 27(2), 227-235(2020)). In addition, many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is the degenerate poly-type 2 Euler polynomials and numbers. This focus stems from their importance for applications in combinatorics, number theory and in other aspects of applied mathematics. we construct a new type of degenerate poly-type 2 Euler polynomials by using the degenerate polylogarithm function, called degenerate poly-type 2 Euler polynomials and numbers. We also show several combinatorial identities related to the degenerate poly-type 2 Euler polynomials and numbers. We also construct the degenerate unipolytype 2 Euler polynomials attached to an arithmetic function. By using the degenerate polylogarithm function, we also give some new explicit expressions and identities related to degenerate unipoly-type 2 Euler polynomials and some special numbers and polynomials.
참고문헌 (31)
- Araci, S., "Extended q-Dedekind-type Daehee-Changhee sums associated with extended q-Euler polynomials", Adv. Difference Equ, 2015, pp.272~ (2015)
- Serkan Araci, "A NOTE ON THE q-ANALOGUE OF KIM’S p-ADIC log GAMMA TYPE FUNCTIONS ASSOCIATED WITH q-EXTENSION OF GENOCCHI AND EULER NUMBERS WITH WEIGHT α", 대한수학회보, 50(2), pp.583~588 (2013), 대한수학회
- Araci, S, "Explicit formulas involving q-Euler numbers and polynomials", Abstr. Appl. Anal, pp.298531~ (2012)[DOI]
- Brewbaker, C., "Lonesum(0,1)-imatrices and poly-Bernoulli numbers of negative index", Master, pp.2005
- Carlitz, L., "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
- L. Comtet, "Advanced Combinatorics: The Art of Finite and Infinite Expansions" (1974), Reidel
- D. V. Dolgy, "SOME EXPLICIT FORMULAS OF DEGENERATE STIRLING NUMBERS ASSOCIATED WITH THE DEGENERATE SPECIAL NUMBERS AND POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 21(2), pp.309~317 (2018), 장전수학회[DOI]
- Hardy, G.H., "On a class a functions", Proc. London Math. Soc, 3, pp.441~460 (1905)
- Jolany, H., "More Properties of multipoly - Euler polynomials", Bol.Soc.Math.Mexo, 21, pp.149~162 (2015)
- Jonqui`ere, A., "Note sur la serie Σ1n=1xn ns", Bull. Soc. Math. France, 17, pp.142~152 (1889)
- 장관우, "A note on type 2 degenerate Euler and Bernoulli polynomials", Advanced Studies in Contemporary Mathematics, 29(1), pp.147~159 (2019), 장전수학회[DOI]
- Kaneko, M., "Poly-Bernoulli numbers", J.Th´eor. Nombres Bordeaux, 9, pp.221~228 (1997)
- Lewin, L., "Polylogarithms and associated functions", pp.xvii+359~ (1981), North-Holland Publishing Co
- Kim, D.S., "A note on polyexponential amd unipoly functions", Russ. J. Math. Phys, 26(1), pp.40~49 (2019)
- Kim, D.S., "A note on a new type of degenerate Bernoulli numbers", Russ. J. Math. Phys, 27(2), pp.227~235 (2020)
- Kim, D.S, "Identities of symmetry for type 2 Bernoulli and Euler polynomials", Symmetry, 11, pp.613~ (2020)
- Kim, D.S., "Some applications of degenerate poly-Bernoulli numbers and polynomials", Georgian Math. J, pp.415~421 (2019)
- 김택연, "A note on degenerate stirling polynomials of the second kind", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(3), pp.319~332 (2017), 장전수학회[DOI]
- Kim, T., "Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials", Adv. Difference Equ, 168, pp.12~ (2020)
- Kim, T., "Degenerate poly-Bernoulli numbers and polynomials", Informatica, 31(3), pp.1~7 (2020)
- Kim, T., "On type 2 degenerate Bernoulli and Euler polynomials of complex variable", Adv. Difference Equ, 490, pp.15~ (2019)
- Kim, T., "Some identities on type2 degenerate Bernoulli polynomials of the second kind", symmetry, 12, pp.510~ (2020)
- Kim, T., "Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae-Stirling numbers", Adv. Difference Equ, 245(2020) (2020)
- Kim, T., "Some relations of two type 2 polynomials and discrete harmonic numbers and polynomials", Symmetry, 12(6), pp.905~ (2020)
- Kim, T., "Degenerate Laplace transform and degenerate gamma function", Russ. J. Math. Phys, 24(2), pp.241~248 (2017)
- Kim, T., "Note on the degenerate gamma function", Russ. J. Math. Phys, 27(3), pp.352~358 (2020)
- Kim, T., "λ-Analogue of Stiring polynomials of the second kind", Proc. Jangjeong Math. Soc, 20(3), pp.319~331 (2017)
- Ohno, Y., "On the party of poly-Euler numbers", RIMS Kˆokuˆuroku Bessatsu, B32, pp.271~278 (2012)
- Romam, S., "The Umbral calculus, Pure and Appliied Math. 111", pp.x+193~ (1984), Academic Press Inc
- Yoshinori, H., "Poly-Euler polynomials and Arakawa-Kaneko type zeta funtions", Funtiones et Approximatio, 1(1), pp.7~22 (2014)
- Zagier, D., "The Bloch-Wigner-Ramakrishnan polylogarithm function", Math. Ann, 286(1-3), pp.613~624 (1990)