Results 31 to 40 of about 4,091,594 (313)

Two Nice Determinantal Expressions and A Recurrence Relation for the Apostol--Bernoulli Polynomials

, 2017
In the paper, the authors establish two nice determinantal expressions and a recurrence relation for the Apostol--Bernoulli polynomials.
Feng Qi (祁锋), Bai-Ni Guo (郭白妮)
semanticscholar   +1 more source

Sequences of twice-iterated Δw-Gould–Hopper Appell polynomials

Journal of Taibah University for Science
In this paper, we introduce general sequence of twice-iterated [Formula: see text]-(degenerate) Gould–Hopper Appell polynomials (TI-DGHAP) via discrete [Formula: see text]-Gould–Hopper Appell convolution. We obtain some of their characteristic properties
Neslihan Biricik, Bayram Çekim, Mehmet Ali Özarslan   +2 more
doaj   +1 more source

A formal operator involving Fermatian numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In this note, old and new properties of Fermatian numbers _zₙ= (1-zⁿ)/(1-z) are recalled. A new formal operator is defined and some identities and extensions are discussed.
Carlos M. da Fonseca, Anthony G. Shannon
doaj   +1 more source

Complexity of Some Duplicating Networks

IEEE Access, 2021
There are plentiful ways to duplicate a graph (network), such as splitting, shadow, mirror, and total graph. In this paper, we derive an evident formula of the complexity, a number of spanning trees, of the closed helm graph, the mirror graph of the path
Mohamed R. Zeen El Deen, Walaa A. Aboamer   +1 more
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On the Song recurrence relation for the Riemann zeta function

, 2017
In this paper, the author uses the generating function for the Bernoulli numbers in order to obtain a new proof for a known linear recurrence relation of the Riemann zeta function with even integer arguments, .2n/. 2010 Mathematics Subject Classification:
M. Merca
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Recurrence relation for relativistic atomic matrix elements

, 2000
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully ...
A L Salas-Brito, Bjorken J D, Blanchard P, Bluhm R, Constantinescu F, De Lange O L, Grant I P, Greiner W, H N Núñez-Yépez, Kobus J, Martínez-y-Romero R P, Martínez-y-Romero R P, Moss R E, Núñez-Yépez H N, Pasternack S, Quiney H M, R P Martínez-y-Romero   +16 more
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Two variables generalized Laguerre polynomials

Karpatsʹkì Matematičnì Publìkacìï, 2021
The objective of this paper is to introduce and study the generalized Laguerre polynomial for two variables. We prove that these polynomials are characterized by the generalized hypergeometric function.
A. Asad
doaj   +1 more source

Fast calculation of computer-generated hologram using run-length encoding based recurrence relation.

Optics Express, 2015
Computer-Generated Holograms (CGHs) can be generated by superimposing zoneplates. A zoneplate is a grating that can concentrate an incident light into a point.
Takashi Nishitsuji, T. Shimobaba, T. Kakue, T. Ito   +3 more
semanticscholar   +1 more source

Computing recurrence coefficients of multiple orthogonal polynomials

, 2015
Multiple orthogonal polynomials satisfy a number of recurrence relations, in particular there is a $(r+2)$-term recurrence relation connecting the type II multiple orthogonal polynomials near the diagonal (the so-called step-line recurrence relation) and
Filipuk, Galina, Haneczok, Maciej, Van Assche, Walter   +2 more
core   +1 more source

The mathematics of generalized Fibonacci sequences: Binet's formula and identities [PDF]

Mathematica Moravica
This article considers a generalized Fibonacci sequence {Vn} with general initial conditions, V0 = a, V1 = b, and a versatile recurrence relation Vn = pVn-1 + qVn-2, where n ≥ 2 and a, b, p and q are any non-zero real numbers. The generating function and
Verma K.L.
doaj   +1 more source