Jindalrae and Gaenari numbers and polynomials

The aim of this paper is to study Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae-Stirling numbers of the first and second kinds. For this purpose, we first introduce Jindalrae-Stirling numbers of the first and second kinds as extensions of the notions of the degenerate Stirling numbers of the first and second kinds, and deduce several relations involving those special numbers. Then we introduce Jindalrae and Gaenari numbers and polynomials and obtain some explicit expressions and identities associated with those numbers and polynomials. In addition, we interpret our results by using umbral calculus.

[1]  Taekyun Kim,et al.  Degenerate binomial coefficients and degenerate hypergeometric functions , 2020 .

[2]  Taekyun Kim,et al.  Some Identities of Degenerate Bell Polynomials , 2020, Mathematics.

[3]  Powers under umbral composition and degeneration for Sheffer sequences , 2016 .

[4]  Dae San Kim,et al.  Degenerate polyexponential functions and degenerate Bell polynomials , 2020, Journal of Mathematical Analysis and Applications.

[5]  Leonard Carlitz,et al.  A degenerate Staudt-Clausen theorem , 1956 .

[6]  Serkan Araci,et al.  A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials , 2012, 1205.6590.

[7]  Mourad E. H. Ismail,et al.  A -umbral calculus , 1981 .

[8]  Dae San Kim,et al.  Degenerate Stirling Polynomials of the Second Kind and Some Applications , 2019, Symmetry.

[9]  Taekyun Kim,et al.  SOME IDENTITIES FOR BERNOULLI NUMBERS OF THE SECOND KIND ARISING FROM A NON-LINEAR DIFFERENTIAL EQUATION , 2015 .

[10]  Taekyun Kim,et al.  Identities of Symmetry for Degenerate Euler Polynomials and Alternating Generalized Falling Factorial Sums , 2017 .

[11]  Taekyun Kim,et al.  Some identities of extended degenerate r-central Bell polynomials arising from umbral calculus , 2019, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas.

[12]  Taekyun Kim.  A note on degenerate stirling polynomials of the second kind , 2017 .

[13]  H. Srivastava.  Some families of generating functions associated with the Stirling numbers of the second kind , 2000 .

[14]  T. Kim,et al.  A Note on a New Type of Degenerate Bernoulli Numbers , 2020 .

[15]  Seog-Hoon Rim,et al.  On finite-times degenerate Cauchy numbers and polynomials , 2015 .

[16]  Ma Minyoung,et al.  Some identities on the fully degenerate Bell polynomials of the second kind , 2020 .

[17]  A note on modified degenerate q-Daehee polynomials and numbers , 2019, Journal of Inequalities and Applications.

[18]  Taekyun Kim,et al.  Degenerate r-Stirling Numbers and r-Bell Polynomials , 2018 .

[19]  Lee-Chae Jang,et al.  A Note on Discrete Degenerate Random Variables , 2019 .

[20]  M. Saif,et al.  Evaluation of Apostol–Euler Based Poly Daehee Polynomials , 2019, International Journal of Applied and Computational Mathematics.