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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Convolution | 33C50 | Mathematics, general | Mathematics | Bernoulli polynomials | 11B68 | Central factorials | MATHEMATICS | MATHEMATICS, APPLIED | JACOBI-STIRLING NUMBERS

Journal Article

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