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中国科学:数学英文版, ISSN 1674-7283, 2015, Volume 58, Issue 10, pp. 2095 - 2104
We investigate Bell polynomials, also called Touchard polynomials or exponential polynomials, by using and without using umbral calculus. We use three... 
恒等式 | 指数多项式 | 阶乘 | Bell多项式 | 贝尔 | 伯努利多项式 | 哑演算 | 柯西 | 11B83 | 05A40 | umbral calculus | Cauchy polynomial | 11B73 | higher-order Bernoulli polynomial | 05A19 | Mathematics | Applications of Mathematics | Bell-polynomial | poly-Bernoulli polynomial | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 03/2018, Volume 14, Issue 2, pp. 595 - 613
We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see... 
finite summation | p-Bernoulli polynomial | Bernoulli polynomial | geometric polynomial | poly-Bernoulli polynomial
Journal Article
Journal of Number Theory, ISSN 0022-314X, 10/2014, Volume 143, pp. 142 - 161
The Arakawa–Kaneko zeta functions interpolate the poly-Bernoulli numbers at the negative integers and their values at positive integers are connected to... 
Arakawa–Kaneko zeta functions | Euler sums | Poly-Bernoulli polynomials | Barnes zeta functions | Bernoulli polynomials | Hurwitz zeta function | Arakawa-Kaneko zeta functions | MATHEMATICS | MULTIPLE ZETA | NUMBERS | GAMMA-FUNCTIONS | VALUES
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 08/2016, Volume 12, Issue 5, pp. 1295 - 1309
We evaluate the ordinary convolution of Bernoulli polynomials in closed form in terms of poly-Bernoulli polynomials. As applications we derive identities for p... 
poly-Bernoulli polynomials | Bernoulli polynomials | convolution identities | p-adic analysis | Arakawa-Kaneko zeta functions | MATHEMATICS | MULTIPLE ZETA | NUMBERS | VALUES
Journal Article
Journal of Computational Analysis and Applications, ISSN 1521-1398, 06/2019, Volume 26, Issue 6, pp. 1070 - 1083
Journal Article
Journal of Computational Analysis and Applications, ISSN 1521-1398, 07/2019, Volume 26, Issue 8, pp. 1387 - 1400
Journal Article
Kyushu Journal of Mathematics, ISSN 1340-6116, 2011, Volume 65, Issue 1, pp. 15 - 24
In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. We call them poly-Bernoulli... 
poly-Bernoulli polynomials | zeta functions | polylogarithms | poly-Bernoulli numbers | Poly-Bernoulli polynomials | Zeta functions | Poly-Bernoulli numbers | Polylogarithms | MATHEMATICS | FORMULA
Journal Article
Journal of Number Theory, ISSN 0022-314X, 07/2015, Volume 152, pp. 38 - 54
We define poly-Bernoulli numbers and polynomials with a q parameter. These numbers and polynomials show a correspondence to poly-Cauchy numbers and polynomials... 
Poly-Bernoulli and poly-Cauchy numbers and polynomials | Congruences | λ-Stirling numbers | Weighted Stirling numbers | MATHEMATICS | STIRLING NUMBERS | A-Stirling numbers | CAUCHY NUMBERS
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 03/2017, Volume 13, Issue 2, pp. 371 - 391
By using the restricted and associated Stirling numbers of the first kind, we define the generalized restricted and associated poly-Cauchy polynomials. By... 
restricted stirling numbers | incomplete poly-Cauchy polynomials | Incomplete poly-Bernoulli polynomials | associated stirling numbers | MATHEMATICS | STIRLING NUMBERS
Journal Article
Acta Scientiarum Mathematicarum, ISSN 0001-6969, 2014, Volume 80, Issue 3-4, pp. 373 - 388
Journal Article
08/2017, Volume 26, Issue 3, 7
In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with a polylogarithmic function and a p-adic invariant integral on... 
11B83 | 11S80 | 05A40 | MATHEMATICS | Degenerate poly-Bernoulli polynomial | p-adic invariant integral | EULER | umbral calculus
Book Chapter
Fasciculi Mathematici, ISSN 0044-4413, 07/2017, Volume 58, Issue 1, pp. 97 - 112
In this paper, we introduce a new class of Hermite multiple-poly-Bernoulli numbers and polynomials of the second kind and investigate some properties for these... 
multi-poly-Bernoulli polynomials of the second kind | Hermite polynomials | symmetric identities | summation formulae | Hermite multi-poly-Bernoulli polynomials of the second kind
Journal Article
Journal of Computational Analysis and Applications, ISSN 1521-1398, 2018, Volume 25, Issue 7, pp. 1307 - 1323
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 8
Journal Article
Journal of Computational Analysis and Applications, ISSN 1521-1398, 2016, Volume 21, Issue 5, pp. 856 - 870
In this paper, we consider the Barnes' multiple Frobenius-Euler and Hermite mixed-type polynomials. Using the umbral calculus, we derive several explicit... 
Barnes’ multiple Frobenius-Euler and Hermite mixed-type polynomials | Umbral calculus | MATHEMATICS, APPLIED | BERNOULLI POLYNOMIALS | COMPUTER SCIENCE, THEORY & METHODS | Barnes' multiple Frobenius-Euler and Hermite mixed-type polynomials | umbral calculus | POLY-BERNOULLI
Journal Article
Journal of Computational Analysis and Applications, ISSN 1521-1398, 2016, Volume 21, Issue 5, pp. 954 - 966
In this paper, we introduce the degenerate poly-Bernoulli polynomials of the second kind, which reduce in the limit to the poly-Bernoulli polynomials of the... 
Degenerate Poly-Bernoulli polynomials | Umbral calculus | ORDER | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | EULER POLYNOMIALS
Journal Article
Mathematics, ISSN 2227-7390, 01/2019, Volume 7, Issue 2, p. 121
We firstly consider the fully degenerate Gould-Hopper polynomials with a q parameter and investigate some of their properties including difference rule,... 
Polylogarithm functions | Stirling numbers of second kind | Gould-Hopper polynomials | Cauchy product | Bernoulli polynomials | Poly Bernoulli polynomials | Hermite polynomials | MATHEMATICS | EXTENSIONS | IDENTITIES | HERMITE | poly Bernoulli polynomials | Gould–Hopper polynomials
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 13
In this paper, we consider the degenerate poly-Bernoulli polynomials. We present several explicit formulas and recurrence relations for these polynomials.... 
11B83 | 05A40 | Analysis | umbral calculus | Mathematics, general | 05A19 | Mathematics | Applications of Mathematics | degenerate poly-Bernoulli polynomials | MATHEMATICS | MATHEMATICS, APPLIED | BERNSTEIN | Calculus | Polynomials | Mathematical analysis | Inequalities
Journal Article
Lithuanian Mathematical Journal, ISSN 0363-1672, 10/2017, Volume 57, Issue 4, pp. 490 - 505
Journal Article
Filomat, ISSN 0354-5180, 2016, Volume 30, Issue 4, pp. 1029 - 1035
In this paper, we consider the fully degenerate poly-Bernoulli polynomials with a q parameter. We present several properties, explicit formulas and recurrence... 
Fully degenerate poly-Bernoulli polynomials with a q parameter | Umbral calculus | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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