scholarly journals On some q-versions of the Ramanujan Master Theorem

2019 ◽  
Vol 50 (2) ◽  
pp. 433-458
Author(s):  
Ahmed Fitouhi ◽  
Kamel Brahim ◽  
Néji Bettaibi
Keyword(s):  
Master Theorem

Ramanujan’s Master Theorem

2012 ◽  
Vol 29 (1-3) ◽  
pp. 103-120 ◽  
Author(s):  
Tewodros Amdeberhan ◽  
Olivier Espinosa ◽  
Ivan Gonzalez ◽  
Marshall Harrison ◽  
Victor H. Moll ◽  
...  
Keyword(s):  
Master Theorem

scholarly journals Ramanujan's Master Theorem applied to the evaluation of Feynman diagrams

2015 ◽  
Vol 63 ◽  
pp. 214-230 ◽  
Author(s):  
Ivan Gonzalez ◽  
Victor H. Moll ◽  
Ivan Schmidt
Keyword(s):  
Feynman Diagrams ◽  
Master Theorem

scholarly journals Zeons, Permanents, the Johnson Scheme, and Generalized Derangements

2011 ◽  
Vol 2011 ◽  
pp. 1-29 ◽  
Author(s):  
Philip Feinsilver ◽  
John McSorley
Keyword(s):  
Linear Combination ◽  
Exponential Distribution ◽  
Trace Formula ◽  
Association Scheme ◽  
Permutation Groups ◽  
Identity Matrix ◽  
Johnson Scheme ◽  
Master Theorem

Starting with the zero-square “zeon algebra,” the connection with permanents is shown. Permanents of submatrices of a linear combination of the identity matrix and all-ones matrix lead to moment polynomials with respect to the exponential distribution. A permanent trace formula analogous to MacMahon's master theorem is presented and applied. Connections with permutation groups acting on sets and the Johnson association scheme arise. The families of numbers appearing as matrix entries turn out to be related to interesting variations on derangements. These generalized derangements are considered in detail as an illustration of the theory.

scholarly journals COMBINATORICS AND N-KOSZUL ALGEBRAS

2008 ◽  
Vol 05 (08) ◽  
pp. 1205-1214
Author(s):  
ROLAND BERGER
Keyword(s):  
Hilbert Series ◽  
Natural Generalization ◽  
Koszul Algebras ◽  
Polynomial Algebras ◽  
New Type ◽  
Master Theorem

The numerical Hilbert series combinatorics for quadratic Koszul algebras was extended to N-Koszul algebras by Dubois-Violette and Popov [9]. In this paper, we give a striking application of this extension when the relations of the algebra are all the antisymmetric tensors of degree N over given variables. Furthermore, we present a new type of Hilbert series combinatorics, called comodule Hilbert series combinatorics, and due to Hai, Kriegk and Lorenz [15]. When the relations are all the antisymmetric tensors, a natural generalization of the MacMahon Master Theorem (MMT) is obtained from the comodule level, the original MMT corresponding to N = 2 and to polynomial algebras.

scholarly journals Koszul algebras and the quantum MacMahon master theorem

2007 ◽  
Vol 39 (4) ◽  
pp. 667-676 ◽  
Author(s):  
Phùng Hô Hai ◽  
Martin Lorenz
Keyword(s):  
Koszul Algebras ◽  
Master Theorem

scholarly journals Triple integral identities and zeta functions

2010 ◽  
Vol 4 (2) ◽  
pp. 347-360
Author(s):  
Anthony Sofo
Keyword(s):  
Closed Form ◽  
Zeta Functions ◽  
Harmonic Numbers ◽  
Binomial Sums ◽  
Integral Identities ◽  
Master Theorem

Some new identities are given for the representation of binomial sums. A master theorem is developed from which integral and closed form results, in terms of Zeta functions and harmonic numbers, are developed for sums of the type ?n?1 tn/n4(an+j/j)(bn+k/k)(cn+l/l).

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