SAE technical paper series, Volume 929396.

Free-piston Stirling power converters are a candidate for high capacity space power applications. The Space Power Research Engine (SPRE), a free-piston...

Stirling engines

Stirling engines

eJournal

Computers and Mathematics with Applications, ISSN 0898-1221, 2006, Volume 51, Issue 3, pp. 631 - 642

Recently, Srivastava and Pintér [1] investigated several interesting properties and relationships involving the classical as well as the generalized (or...

Euler polynomials and numbers | ernoulli polynomials and numbers | Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers, Stirling numbers of the second kind, Generating functions, Srivastava-Pintér addition theorems, Recursion formulas | Generalized (or higher-order) Bernoulli polynomials and numbers | Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers | Bernoulli polynomials and numbers | MATHEMATICS, APPLIED | generalized (or higher-order) Euler polynomials and numbers | stirling numbers of the second kind | generalized Apostol-Bernoulli polynomials and numbers | Srivastava-Pinter addition theorems | generating functions | generalized (or higher-order) Bernoulli polynomials and numbers | generalized Apostol-Euler polynomials and numbers | recursion formulas | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Apostol-Euler polynomials and numbers | Apostol-Bernoulli polynomials and numbers | Mathematical models

Euler polynomials and numbers | ernoulli polynomials and numbers | Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers, Stirling numbers of the second kind, Generating functions, Srivastava-Pintér addition theorems, Recursion formulas | Generalized (or higher-order) Bernoulli polynomials and numbers | Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers | Bernoulli polynomials and numbers | MATHEMATICS, APPLIED | generalized (or higher-order) Euler polynomials and numbers | stirling numbers of the second kind | generalized Apostol-Bernoulli polynomials and numbers | Srivastava-Pinter addition theorems | generating functions | generalized (or higher-order) Bernoulli polynomials and numbers | generalized Apostol-Euler polynomials and numbers | recursion formulas | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Apostol-Euler polynomials and numbers | Apostol-Bernoulli polynomials and numbers | Mathematical models

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 05/2017, Volume 40, Issue 7, pp. 2347 - 2361

The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial...

functional equations | central factorial numbers | binomial coefficients | array polynomials | Euler numbers and polynomials | generating functions | binomial sum | Stirling numbers | combinatorial sum | MATHEMATICS, APPLIED | IDENTITIES | ARRAY TYPE POLYNOMIALS | GENERATING-FUNCTIONS | BERNOULLI | Computation | Factorials | Mathematical analysis | Mathematical models | Polynomials | Arrays | Combinatorial analysis | Sums | Mathematics - Number Theory

functional equations | central factorial numbers | binomial coefficients | array polynomials | Euler numbers and polynomials | generating functions | binomial sum | Stirling numbers | combinatorial sum | MATHEMATICS, APPLIED | IDENTITIES | ARRAY TYPE POLYNOMIALS | GENERATING-FUNCTIONS | BERNOULLI | Computation | Factorials | Mathematical analysis | Mathematical models | Polynomials | Arrays | Combinatorial analysis | Sums | Mathematics - Number Theory

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 12/2017, Volume 91, Issue 6, pp. 1055 - 1071

In this paper we introduce restricted r-Stirling numbers of the first kind. Together with restricted r-Stirling numbers of the second kind and the associated...

Combinatorial identities | Generating function | Mathematics | Secondary 11B68 | Primary 11B83 | Analysis | Poly-Bernoulli numbers | 11B73 | 05A19 | Combinatorics | Incomplete r -Stirling numbers | 05A15 | Poly-Cauchy numbers | Incomplete r-Stirling numbers | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | BESSEL NUMBERS | COMBINATORICS

Combinatorial identities | Generating function | Mathematics | Secondary 11B68 | Primary 11B83 | Analysis | Poly-Bernoulli numbers | 11B73 | 05A19 | Combinatorics | Incomplete r -Stirling numbers | 05A15 | Poly-Cauchy numbers | Incomplete r-Stirling numbers | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | BESSEL NUMBERS | COMBINATORICS

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 8/2016, Volume 149, Issue 2, pp. 306 - 323

By using the restricted Stirling numbers and associated Stirling numbers, we introduce two kinds of incomplete Cauchy numbers, which are generalizations that...

secondary 05A15 | restricted Stirling number | Mathematics, general | associated Stirling number | 11B75 | 05A19 | Mathematics | primary 11B73 | Cauchy number | Stirling number | 05A18 | MATHEMATICS | STIRLING NUMBERS | Information science | Statistics

secondary 05A15 | restricted Stirling number | Mathematics, general | associated Stirling number | 11B75 | 05A19 | Mathematics | primary 11B73 | Cauchy number | Stirling number | 05A18 | MATHEMATICS | STIRLING NUMBERS | Information science | Statistics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 03/2019, Volume 342, Issue 3, pp. 628 - 634

The orthogonality of the (q,t)-version of the Stirling numbers has recently been proved by Cai and Readdy using a bijective argument. In this paper, we...

Stirling numbers | Recurrence relations | [formula omitted]-analogues | [Formula presented]-analogues | MATHEMATICS | Q-STIRLING NUMBERS | Q-ANALOGS | (q, t)-analogues | CUBES | SUMS

Stirling numbers | Recurrence relations | [formula omitted]-analogues | [Formula presented]-analogues | MATHEMATICS | Q-STIRLING NUMBERS | Q-ANALOGS | (q, t)-analogues | CUBES | SUMS

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 6/2016, Volume 180, Issue 2, pp. 271 - 288

By using the restricted and associated Stirling numbers of the first kind by generalizing the (unsigned) Stirling numbers of the first kind, we define the...

Restricted Stirling numbers | Secondary 11B75 | Restricted poly-Cauchy numbers | Mathematics, general | Associated Stirling numbers | 05A19 | Mathematics | Primary 11B73 | Associated poly-Cauchy numbers | 05A15 | Poly-Cauchy numbers | MATHEMATICS | BERNOULLI NUMBERS

Restricted Stirling numbers | Secondary 11B75 | Restricted poly-Cauchy numbers | Mathematics, general | Associated Stirling numbers | 05A19 | Mathematics | Primary 11B73 | Associated poly-Cauchy numbers | 05A15 | Poly-Cauchy numbers | MATHEMATICS | BERNOULLI NUMBERS

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2018, Volume 12, Issue 1, pp. 1 - 35

The main purpose of this paper is to construct new families of special numbers with their generating functions. These numbers are related to many well-known...

Integers | Numbers | Generating function | Factorials | Discrete mathematics | Polynomials | Coefficients | Combinatorics | New family | Combinatorial sum | Central factorial numbers | Bernoulli numbers | Binomial coefficients | Euler numbers | Functional equations | Generating functions | Array polynomials | Stirling numbers | Fibonacci numbers | MATHEMATICS, APPLIED | COMBINATORIAL SUMS | Q-BERNOULLI NUMBERS | GENERATING-FUNCTIONS | MATHEMATICS

Integers | Numbers | Generating function | Factorials | Discrete mathematics | Polynomials | Coefficients | Combinatorics | New family | Combinatorial sum | Central factorial numbers | Bernoulli numbers | Binomial coefficients | Euler numbers | Functional equations | Generating functions | Array polynomials | Stirling numbers | Fibonacci numbers | MATHEMATICS, APPLIED | COMBINATORIAL SUMS | Q-BERNOULLI NUMBERS | GENERATING-FUNCTIONS | MATHEMATICS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2011, Volume 217, Issue 12, pp. 5702 - 5728

Recently, the authors introduced some generalizations of the Apostol–Bernoulli polynomials and the Apostol–Euler polynomials (see [Q.-M. Luo, H.M. Srivastava,...

Lerch’s functional equation | Hurwitz (or generalized), Hurwitz–Lerch and Lipschitz–Lerch zeta functions | Srivastava’s formula and Gaussian hypergeometric function | Genocchi numbers and Genocchi polynomials of higher order | Stirling numbers and the λ-Stirling numbers of the second kind | Apostol–Genocchi numbers and Apostol–Genocchi polynomials of higher order | Apostol–Bernoulli polynomials and Apostol–Euler polynomials of higher order | Apostol–Genocchi numbers and Apostol–Genocchi polynomials | Apostol-Bernoulli polynomials and Apostol-Euler polynomials of higher order | Srivastava's formula and Gaussian hypergeometric function | Hurwitz (or generalized), Hurwitz-Lerch and Lipschitz-Lerch zeta functions | Apostol-Genocchi numbers and Apostol-Genocchi polynomials | Apostol-Genocchi numbers and Apostol-Genocchi polynomials of higher order | Lerch's functional equation | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | IDENTITIES | Q-EXTENSIONS | BERNOULLI | EXPLICIT FORMULA | ORDER | Stirling numbers and the lambda-Stirling numbers of the second kind | EULER POLYNOMIALS | INTEGRAL-REPRESENTATIONS | Hypergeometric functions | Analogue | Computation | Mathematical analysis | Gaussian | Mathematical models | Error correction | Representations

Lerch’s functional equation | Hurwitz (or generalized), Hurwitz–Lerch and Lipschitz–Lerch zeta functions | Srivastava’s formula and Gaussian hypergeometric function | Genocchi numbers and Genocchi polynomials of higher order | Stirling numbers and the λ-Stirling numbers of the second kind | Apostol–Genocchi numbers and Apostol–Genocchi polynomials of higher order | Apostol–Bernoulli polynomials and Apostol–Euler polynomials of higher order | Apostol–Genocchi numbers and Apostol–Genocchi polynomials | Apostol-Bernoulli polynomials and Apostol-Euler polynomials of higher order | Srivastava's formula and Gaussian hypergeometric function | Hurwitz (or generalized), Hurwitz-Lerch and Lipschitz-Lerch zeta functions | Apostol-Genocchi numbers and Apostol-Genocchi polynomials | Apostol-Genocchi numbers and Apostol-Genocchi polynomials of higher order | Lerch's functional equation | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | IDENTITIES | Q-EXTENSIONS | BERNOULLI | EXPLICIT FORMULA | ORDER | Stirling numbers and the lambda-Stirling numbers of the second kind | EULER POLYNOMIALS | INTEGRAL-REPRESENTATIONS | Hypergeometric functions | Analogue | Computation | Mathematical analysis | Gaussian | Mathematical models | Error correction | Representations

Journal Article

Publicationes Mathematicae, ISSN 0033-3883, 2016, Volume 88, Issue 3-4, pp. 357 - 368

By using the associated and restricted Stirling numbers of the second kind, we give some generalizations of the poly-Bernoulli numbers. We also study their...

Restricted Stirling numbers | Restricted poly-bernoulli numbers | Bernoulli numbers | Associated poly-bernoulli numbers | Poly-Bernoulli numbers | Stirling numbers | Associated stirling numbers | POLYNOMIALS | MATHEMATICS | associated Stirling numbers | associated poly-Bernoulli numbers | CAUCHY NUMBERS | restricted Stirling numbers | poly-Bernoulli numbers | restricted poly-Bernoulli numbers

Restricted Stirling numbers | Restricted poly-bernoulli numbers | Bernoulli numbers | Associated poly-bernoulli numbers | Poly-Bernoulli numbers | Stirling numbers | Associated stirling numbers | POLYNOMIALS | MATHEMATICS | associated Stirling numbers | associated poly-Bernoulli numbers | CAUCHY NUMBERS | restricted Stirling numbers | poly-Bernoulli numbers | restricted poly-Bernoulli numbers

Journal Article

Discrete Mathematics, ISSN 0012-365X, 10/2015, Volume 338, Issue 10, pp. 1660 - 1666

In this paper we present a detailed study of r-Lah numbers, which give the number of partitions of a finite set into a fixed number of nonempty ordered subsets...

[formula omitted]-Lah numbers | r-Lah numbers | MATHEMATICS | STIRLING NUMBERS

[formula omitted]-Lah numbers | r-Lah numbers | MATHEMATICS | STIRLING NUMBERS

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 2019, Volume 158, Issue 1, pp. 159 - 172

We investigate mixed partitions with extra condition on the sizes of the blocks. We give a general formula and the generating function. We consider in more...

Stirling number of the second kind | multiplicative partition function | mixed partition of a set | MATHEMATICS | Statistics | Social service

Stirling number of the second kind | multiplicative partition function | mixed partition of a set | MATHEMATICS | Statistics | Social service

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

Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 15, pp. 2337 - 2348

Let G be a finite group of order m≥1. A Dowling lattice Qn(G) is the geometric lattice of rank n over G. In this paper, we define the r-Whitney numbers of the...

Lah numbers | Whitney numbers | Dowling lattice | [formula omitted]-Stirling numbers | Dowling polynomials | Riordan group | r-Stirling numbers | MATHEMATICS | RIORDAN ARRAYS | Statistics | Questions and answers

Lah numbers | Whitney numbers | Dowling lattice | [formula omitted]-Stirling numbers | Dowling polynomials | Riordan group | r-Stirling numbers | MATHEMATICS | RIORDAN ARRAYS | Statistics | Questions and answers

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 281 - 297

The aim of this paper is to construct interpolation functions for the numbers of the k-ary Lyndon words which count n digit primitive necklace class...

Lyndon words | 03D40 | Arithmetical functions | Special polynomials | Frobenius–Euler numbers and polynomials | 11S40 | Theoretical, Mathematical and Computational Physics | 11M35 | Generating functions | 68R15 | Mathematics | Algorithm | 11A25 | 11B68 | Stirling numbers of the first kind | 47E05 | 11B83 | Mathematics, general | Apostol–Euler numbers and polynomials | Differential operator | Applications of Mathematics | Special numbers | 05A05 | 05A15 | MATHEMATICS | Apostol-Euler numbers and polynomials | BERNOULLI | Frobenius-Euler numbers and polynomials | Operators (mathematics) | Interpolation | Algorithms | Infinite series | Combinatorial analysis | Sums

Lyndon words | 03D40 | Arithmetical functions | Special polynomials | Frobenius–Euler numbers and polynomials | 11S40 | Theoretical, Mathematical and Computational Physics | 11M35 | Generating functions | 68R15 | Mathematics | Algorithm | 11A25 | 11B68 | Stirling numbers of the first kind | 47E05 | 11B83 | Mathematics, general | Apostol–Euler numbers and polynomials | Differential operator | Applications of Mathematics | Special numbers | 05A05 | 05A15 | MATHEMATICS | Apostol-Euler numbers and polynomials | BERNOULLI | Frobenius-Euler numbers and polynomials | Operators (mathematics) | Interpolation | Algorithms | Infinite series | Combinatorial analysis | Sums

Journal Article

ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 04/2019, Volume 26, Issue 2

We exhibit a connection between two statistics on set partitions, the intertwining number and the depth-index. In particular, results link the intertwining...

MATHEMATICS | Q-STIRLING NUMBERS | INVOLUTIONS | CHARLIER | MATHEMATICS, APPLIED | ANALOG | CONGRUENCE B-ORBITS

MATHEMATICS | Q-STIRLING NUMBERS | INVOLUTIONS | CHARLIER | MATHEMATICS, APPLIED | ANALOG | CONGRUENCE B-ORBITS

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 04/2017, Volume 24, Issue 2

This paper studies the generalizations of the Stirling numbers of both kinds and the Lah numbers in association with the normal order problem in the Weyl...

Rook numbers | Lah numbers | Normal ordering problem | Stirling numbers | Quasithreshold graphs | MATHEMATICS | MATHEMATICS, APPLIED | quas-ithreshold graphs | BOSON OPERATORS | rook numbers | COMBINATORICS | normal ordering problem

Rook numbers | Lah numbers | Normal ordering problem | Stirling numbers | Quasithreshold graphs | MATHEMATICS | MATHEMATICS, APPLIED | quas-ithreshold graphs | BOSON OPERATORS | rook numbers | COMBINATORICS | normal ordering problem

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2018, Volume 466, Issue 1, pp. 1009 - 1042

In this paper we are interested in Euler-type sums with products of harmonic numbers, Stirling numbers and Bell numbers. We discuss the analytic...

Euler sums | Riemann zeta function | Multiple zeta (star) values | Stirling numbers | Harmonic numbers | Multiple harmonic (star) numbers | INTEGRALS | MATHEMATICS | MULTIPLE ZETA-VALUES | MATHEMATICS, APPLIED | SERIES

Euler sums | Riemann zeta function | Multiple zeta (star) values | Stirling numbers | Harmonic numbers | Multiple harmonic (star) numbers | INTEGRALS | MATHEMATICS | MULTIPLE ZETA-VALUES | MATHEMATICS, APPLIED | SERIES

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2014, Volume 244, pp. 149 - 157

The main objective in this paper is first to establish new identities for the λ-Stirling type numbers of the second kind, the λ-array type polynomials, the...

Bernoulli polynomials and Bernoulli numbers | Apostol–Bernoulli polynomials and Apostol–Bernoulli numbers | [formula omitted]-Stirling numbers of the second kind | [formula omitted]-Array polynomials | [formula omitted]-Bell numbers and [formula omitted]-Bell polynomials | λ-Bell numbers and λ-Bell polynomials | λ-Array polynomials | λ-Stirling numbers of the second kind | Apostol-Bernoulli polynomials and Apostol-Bernoulli numbers | MATHEMATICS, APPLIED | lambda-Array polynomials | lambda-Stirling numbers of the second kind | lambda-Bell numbers and lambda-Bell polynomials | APOSTOL-BERNOULLI | GENERATING-FUNCTIONS | EULER

Bernoulli polynomials and Bernoulli numbers | Apostol–Bernoulli polynomials and Apostol–Bernoulli numbers | [formula omitted]-Stirling numbers of the second kind | [formula omitted]-Array polynomials | [formula omitted]-Bell numbers and [formula omitted]-Bell polynomials | λ-Bell numbers and λ-Bell polynomials | λ-Array polynomials | λ-Stirling numbers of the second kind | Apostol-Bernoulli polynomials and Apostol-Bernoulli numbers | MATHEMATICS, APPLIED | lambda-Array polynomials | lambda-Stirling numbers of the second kind | lambda-Bell numbers and lambda-Bell polynomials | APOSTOL-BERNOULLI | GENERATING-FUNCTIONS | EULER

Journal Article

Journal of Number Theory, ISSN 0022-314X, 06/2016, Volume 163, pp. 238 - 254

In 1935 Carlitz introduced Bernoulli-Carlitz numbers as analogues of Bernoulli numbers for the rational function field Fr(T). In this paper, we introduce...

Cauchy-Carlitz numbers | Stirling-Carlitz numbers | Hasse-Teichmüller derivatives | Bernoulli-Carlitz numbers | MATHEMATICS | Hasse-Teichmuller derivatives

Cauchy-Carlitz numbers | Stirling-Carlitz numbers | Hasse-Teichmüller derivatives | Bernoulli-Carlitz numbers | MATHEMATICS | Hasse-Teichmuller derivatives

Journal Article

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