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International Journal of Number Theory, ISSN 1793-0421, 09/2015, Volume 11, Issue 6, pp. 1807 - 1819
A constructive generalization of Fleck-type Möbius function and inversion via convolution polynomials is presented here. Also provided are certain related... 
inversion formulae | Selberg-multiplicative function | Fleck-type Möbius function | convolution polynomial | Fleck-type Mobius function | MATHEMATICS | FORMULAS
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 11/2014, Volume 42, pp. 112 - 134
Using the basic fact that any formal power series over the real or complex number field can always be expressed in terms of given polynomials {pn(t)}, where... 
SUMMATION FORMULAS | MATHEMATICS | TRIANGLES | INVOLUTIONS | GENERATING-FUNCTIONS | CATALAN NUMBERS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2007, Volume 155, Issue 15, pp. 1895 - 1909
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2009, Volume 58, Issue 7, pp. 1340 - 1348
Two types of symbolic summation formulas are reformulated using an extension of Mullin–Rota’s substitution rule in [R. Mullin, G.-C. Rota, On the foundations... 
Catalan number | Bernoulli number | Generalized harmonic number | Stirling numbers | Delta operator | MATHEMATICS, APPLIED
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2006, Volume 190, Issue 1, pp. 151 - 169
It is shown that a pair of inverse relations can be constructed by the suitable application of Faà di Bruno's formula for finding higher order derivatives of... 
Pair of inverse identities | Faà di Bruno's formula | Formal power series | Inverse relations | inverse relations | MATHEMATICS, APPLIED | POWER | formal power series | Faa di Bruno's formula | pair of inverse identities
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2007, Volume 54, Issue 5, pp. 664 - 678
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 16, pp. 3427 - 3440
Here expounded is a kind of symbolic operator method that can be used to construct many transformation formulas and summation formulas for various types of... 
Generalized Eulerian fractions | Stirling number of the second kind | Power series | Symbolic operator | MATHEMATICS | generalized Eulerian fractions | symbolic operator | stirling number of the second kind | power series
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 04/1998, Volume 20, Issue 3, pp. 366 - 384
It is shown that various well-known generalizations of Stirling numbers of the first and second kinds can be unified by starting with transformations between... 
MATHEMATICS, APPLIED
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2006, Volume 51, Issue 3, pp. 441 - 450
This paper deals with the convergence of the summation of power series of the form Σα≤κ(κ)χ κ, where 0 ≤ α ≤ b ≤ ∞, and { (κ)} is a given sequence of numbers... 
Symbolic summation operator | Euler's series transform, Polya and Szegö identity | Generating function | Power series | symbolic summation operator | generating function | MATHEMATICS, APPLIED | Euler's series transform | Polya and Szego identity | power series | Infinity | Mathematical analysis | Transforms | Symbolic operators | Mathematical models | Transformations | Convergence
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 09/2001, Volume 5, Issue 2, pp. 179 - 196
It is shown that a class of special functions (involving Sheffer-type polynomials and Gegenbauer-Humbert-type polynomials) could have cycle indicator... 
cycle indicator, Cn-representation, Cn-representablity
Journal Article
Fibonacci Quarterly, ISSN 0015-0517, 05/2006, Volume 44, Issue 2, pp. 154 - 165
We investigate a kind of q-analogue which involves a unified generalization of Stirling numbers as a limiting case with q-->1. Some basic properties and... 
MATHEMATICS | 1ST | 2ND KIND | COMBINATORIAL APPLICATIONS | FORMULAS
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2/2006, Volume 73, Issue 1, pp. 79 - 88
We provide a wide class of Mobius inversion formulas in terms of the generalised Mobius functions and their application to the setting of the Selberg... 
MATHEMATICS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 1999, Volume 204, Issue 1, pp. 237 - 247
The main purpose of this paper is to introduce two kinds of generalized Eulerian polynomials and numbers which are associated with the constructions of certain... 
Generalized Eulerian polynomials | Dickson polynomials | Degenerate weighted Stirling numbers | Dickson-Eulerian number | MATHEMATICS | generalized Eulerian polynomials | degenerate weighted Stirling numbers | STIRLING NUMBERS | 2ND KIND
Journal Article
Fibonacci Quarterly, ISSN 0015-0517, 02/1997, Volume 35, Issue 1, pp. 62 - 67
Journal Article
Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 10/1993, Volume 36, Issue 3, pp. 525 - 535
It is shown that an extended Schlomilch formula for Stirling-type pairs of numbers and the inversion formula of Lagrange are implied by each other. Also proved... 
MATHEMATICS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 1993, Volume 123, Issue 1, pp. 3 - 15
This paper gives a brief exposition of several recent results obtained by the authors concerning some classes of inverse relations, including the general... 
MATHEMATICS | MACMAHONS MASTER THEOREM
Journal Article
Analysis in Theory and Applications, ISSN 1672-4070, 12/2005, Volume 21, Issue 4, pp. 359 - 369
We present a constructive generalization of Abel-Gontscharoff’s series expansion to higher dimensions. A constructive application to a problem of multivariate... 
higher dimensional dot product annihilation coefficients | 41A58 | Analysis | Approximations and Expansions | Mathematics | Abel-Gontscharoff-Gould polynomial | multivariate Abel-Gontscharoff interpolation | Abel-Gontscharoff’s Expansion Formula | 13F25 | 41A05
Journal Article
Tohoku Mathematical Journal, Second Series, ISSN 0040-8735, 1991, Volume 43, Issue 2, pp. 235 - 242
It is shown that a certain algebraic identity involving a summation over partitions can be utilized to obtain a class of asymptotic expansions for large... 
formal power series | set of partitions | asymptotic expansion | MATHEMATICS
Journal Article
FIBONACCI QUARTERLY, ISSN 0015-0517, 11/1995, Volume 33, Issue 5, pp. 392 - 397
Journal Article
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