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Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2018, Volume 99, Issue 3, pp. 1 - 7
We prove two conjectural congruences on the (p - 1)th Apery number, which were recently proposed by Z.-H. Sun. 
2010 Mathematics subject classification | primary 11A07 | 11B68 | secondary 05A19 | MATHEMATICS | congruences | Apery numbers | Bernoulli numbers | SUMS
Journal Article
The College Mathematics Journal, ISSN 0746-8342, 01/2020, Volume 51, Issue 1, pp. 25 - 31
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 07/2015, Volume 38, Issue 4, pp. 553 - 562
In this paper, we study the formula for a product of two Euler poly-nomials. From this study, we derive some formulae for the integral of the product of two or... 
Euler numbers and polynomials | 11S80 | Bernoulli numbers | 11B68 | identity | MATHEMATICS
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 02/2020, Volume 43, Issue 2, pp. 203 - 212
In this paper, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities. 
identities | 05A40 | Appell polynomials | Classical umbral calculus | binomial sequences | 11B68 | 70H03 | MATHEMATICS
Journal Article
Experimental Mathematics, ISSN 1058-6458, 10/2018, Volume 27, Issue 4, pp. 437 - 443
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums are... 
11B65 | Faulhaber's theorem | sums of powers of integers | Bernoulli numbers | 11B68 | MATHEMATICS
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 7
In this paper, we study the Fourier series related to higher-order Bernoulli functions and give new identities for higher-order Bernoulli functions which are... 
Analysis | Mathematics, general | Mathematics | Bernoulli polynomials | Applications of Mathematics | 42A16 | Fourier series | 11B68 | Bernoulli functions | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | Inequalities | Research
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 17
In this paper, we study three types of sums of products of ordered Bell and poly-Bernoulli functions and derive their Fourier series expansion. In addition, we... 
ordered Bell function | Fourier series | poly-Bernoulli function | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | Bells | Inequalities | Sums | 11B83 | Research | 42A16 | 11B68
Journal Article
Analysis Mathematica, ISSN 0133-3852, 9/2019, Volume 45, Issue 3, pp. 583 - 598
We introduce polynomial sets of (p, q)-Appell type and give some characterizations of them. The algebraic properties of the set of all polynomial sequences of... 
Appel polynomial | recurrence relation | Mathematics | 33C65 | 11B68 | Analysis | MATHEMATICS
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 14
In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series... 
11B83 | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Fibonacci polynomials | 42A16 | Fourier series | 11B68 | Chebyshev polynomials of the second kind | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | Chebyshev approximation | Polynomials | Mathematical analysis | Fibonacci numbers | Sums | Research
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 01/2018, Volume 29, Issue 1, pp. 43 - 61
We present various identities involving the classical Bernoulli and Euler polynomials. Among others, we prove that and Applications of our results lead to... 
Bernoulli polynomials | Bernoulli numbers | Euler numbers | 11B68 | Euler polynomials | MATHEMATICS | MATHEMATICS, APPLIED | GENERALIZED BERNOULLI | Polynomials
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 844 - 858
In the paper, by induction, the Faà di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher... 
Bell polynomial of the second kind | Tangent number | Bernoulli number | Explicit formula | Derivative polynomial | Euler polynomial | MATHEMATICS, APPLIED | BERNOULLI NUMBERS | INEQUALITIES | IDENTITIES | COMPLETE MONOTONICITY | STIRLING NUMBERS | POLYNOMIALS | EXPLICIT FORMULAS | INTEGRAL-REPRESENTATION | 2ND KIND | 1ST KIND
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 01/2020, Volume 127, Issue 1, pp. 84 - 84
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 13
Several refinements of the Finsler-Hadwiger inequality and its reverse in the triangle are discussed. A new one parameter family of Finsler-Hadwiger... 
Finsler-Hadwiger inequality | triangle inequalities | MATHEMATICS | MATHEMATICS, APPLIED | Triangles | Parameters | Inequalities | Research | 11B68
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 7/2019, Volume 113, Issue 3, pp. 2507 - 2513
Here we study the degenerate central Bell numbers and polynomials as a degenerate version of the recently introduced central Bell numbers and polynomials,... 
Central factorial numbers | 05A68 | Bell numbers | 11B83 | Theoretical, Mathematical and Computational Physics | 11B73 | Mathematics, general | Degenerate central Bell polynomials | Mathematics | Applications of Mathematics | 11B68 | MATHEMATICS | Numbers | Fibonacci numbers | Polynomials
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2019, Volume 291, Issue 3, pp. 1337 - 1356
We prove a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its... 
Weighted sum formulas | Bernoulli numbers | 11M32 | Multiple zeta values | Mathematics, general | Mathematics | Multiple zeta-star values | 11B68 | MATHEMATICS
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2017, Volume 72, Issue 4, pp. 1857 - 1864
By the Lagrange–Bürmann formula, we provide a new explicit formula for determining the coefficients of Ramanujan’s asymptotic expansion for the nth harmonic... 
Lagrange–Bürmann formula | Harmonic number | identity | Mathematics, general | 05A19 | Mathematics | 41A60 | Bernoulli number | 11B68 | asymptotic expansion
Journal Article
Mathematika, ISSN 0025-5793, 2018, Volume 64, Issue 2, pp. 519 - 541
For a positive integer n let Pn=∏pp,sp(n)≥p where p runs over primes and sp(n) is the sum of the base p digits of n. For all n we prove that Pn is divisible by... 
11N37 (primary) | 11B68 (secondary) | MATHEMATICS | MATHEMATICS, APPLIED | NUMBERS | PRIMES | Mathematics - Number Theory
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 7/2016, Volume 107, Issue 1, pp. 9 - 22
The main goal of this paper is the presentation of an elementary analytic technique which enables the evaluation of the so-called restricted sum formulas... 
Restricted sum formulas | Infinite series and products | Primary 11M32 | 11M35 | Generating functions | Riemann zeta function | Mathematics, general | Mathematics | Secondary 11B68 | MATHEMATICS
Journal Article
Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 04/2014, Volume 44, Issue 2, pp. 633 - 648
In this paper we prove that for any prime p\ge 11, {2p-1\choose p-1}\equiv 1 -2p \sum_{k=1}^{p-1}\frac{1}{k} +4p^2\sum_{1\le i\lt j\le... 
11A07 | Wolstenholme's theorem | Congruence | Bernoulli numbers | Wolstenholme prime | 05A10 | prime power | 11B65 | 11B75 | 11B68
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 12/2016, Volume 73, Issue 2, pp. 259 - 264
In the paper, the author presents two finite discrete convolutions that combines central factorial numbers of both kinds and Bernoulli polynomials. 
Convolution | 33C50 | Mathematics, general | Mathematics | Bernoulli polynomials | 11B68 | Central factorials | MATHEMATICS | MATHEMATICS, APPLIED | JACOBI-STIRLING NUMBERS
Journal Article
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