scholarly journals Branching rules for symmetric hypergeometric polynomials

2019 ◽  
Author(s):  
Jan Felipe van Diejen ◽  
Erdal Emsiz
Keyword(s):  
Hypergeometric Polynomials ◽  
Branching Rules

scholarly journals A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1161
Author(s):  
Hari Mohan Srivastava ◽  
Sama Arjika
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Additional Parameter ◽  
Physical Sciences ◽  
General Family ◽  
Hypergeometric Polynomials

Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant.

scholarly journals Zeros of the Hypergeometric Polynomials F(−n, b; −2n; z)

2001 ◽  
Vol 110 (1) ◽  
pp. 74-87 ◽  
Author(s):  
Kathy Driver ◽  
Manfred Möller
Keyword(s):  
Hypergeometric Polynomials

On the zeros of a class of generalized hypergeometric polynomials

2015 ◽  
Vol 253 ◽  
pp. 151-158
Author(s):  
Cleonice F. Bracciali ◽  
Juan José Moreno-Balcázar
Keyword(s):  
Hypergeometric Polynomials

Lie Groups and the Jahn–Teller Effect

1974 ◽  
Vol 52 (11) ◽  
pp. 999-1044 ◽  
Author(s):  
B. R. Judd
Keyword(s):  
Lie Groups ◽  
Nuclear Physics ◽  
Angular Frequency ◽  
Teller Effect ◽  
Octahedral Complex ◽  
Noncompact Group ◽  
Five Dimensions ◽  
Branching Rules ◽  
Jahn Teller ◽  
Jahn Teller Effect

After an introduction to the classic theory of the Jahn–Teller effect for octahedral complexes, an account is given of Lie groups and their relevance to the F+ center in CaO. The coincidence of the three-fold and two-fold vibrational modes (both of angular frequency ω) leads to a study of U5 and R5, the unitary and rotation groups in five dimensions. The language of second quantization is used to describe the weight spaces and branching rules. Pairs of annihilation and creation operators for phonons are coupled to zero angular momentum and used as the generators of the noncompact group O(2, 1). This facilitates the evaluation of matrix elements of V, the interaction that couples the oscillations of the octahedral complex to the electron in its interior. Glauber states are used near the strong Jahn–Teller limit, corresponding to [Formula: see text]. The possible extension of the analysis to incorporate the breathing mode is outlined. Correspondences with problems in nuclear physics are mentioned.

scholarly journals Bilateral Generating Functions Involving Generalized Hypergeometric Polynomials of Two Variables

2017 ◽  
Vol 10 (12) ◽  
pp. 1-5
Author(s):  
P. L. Rama Kameswari ◽  
P. L. Rama Kameswari ◽  
V. S. Bhagavan ◽  
◽  
◽  
...  
Keyword(s):  
Generating Functions ◽  
Hypergeometric Polynomials ◽  
Bilateral Generating Functions

scholarly journals Properties of the zeros of generalized basic hypergeometric polynomials

2015 ◽  
Vol 56 (11) ◽  
pp. 112701 ◽  
Author(s):  
Oksana Bihun ◽  
Francesco Calogero
Keyword(s):  
Hypergeometric Polynomials

scholarly journals Tree Trimming: Four Non-Branching Rules for Priest’s Introduction to Non-Classical Logic

2017 ◽  
Vol 12 (2) ◽  
Author(s):  
Marilynn Johnson
Keyword(s):  
Modal Logic ◽  
Classical Logic ◽  
Variable Domain ◽  
Free Logic ◽  
Intuitionist Logic ◽  
Branching Rule ◽  
Branching Rules ◽  
Graham Priest

In An Introduction to Non-Classical Logic: From If to Is Graham Priest (2008) presents branching rules in Free Logic, Variable Domain Modal Logic, and Intuitionist Logic. I propose a simpler, non-branching rule to replace Priest’s rule for universal instantiation in Free Logic, a second, slightly modified version of this rule to replace Priest’s rule for universal instantiation in Variable Domain Modal Logic, and third and fourth rules, further modifying the second rule, to replace Priest’s branching universal and particular instantiation rules in Intuitionist Logic. In each of these logics the proposed rule leads to tableaux with fewer branches. In Intuitionist logic, the proposed rules allow for the resolution of a particular problem Priest grapples with throughout the chapter. In this paper, I demonstrate that the proposed rules can greatly simplify tableaux and argue that they should be used in place of the rules given by Priest.

Sign in / Sign up

Export Citation Format

Share Document