The Modified Bessel Functions I n (x) of Integer Order

2008 ◽  
pp. 507-517
Author(s):  
Keith B. Oldham ◽  
Jan C. Myland ◽  
Jerome Spanier
Keyword(s):  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Integer Order

scholarly journals A NEW ALGEBRAIC STRUCTURE OF FINITE QUANTUM SYSTEMS AND THE MODIFIED BESSEL FUNCTIONS

2007 ◽  
Vol 04 (07) ◽  
pp. 1205-1215 ◽  
Author(s):  
KAZUYUKI FUJII
Keyword(s):  
Quantum Mechanics ◽  
Algebraic Structure ◽  
Bessel Functions ◽  
Quantum Systems ◽  
Modified Bessel Functions ◽  
Level System ◽  
Integer Order ◽  
Pauli Matrices ◽  
Finite Quantum Systems

In this paper we present a new algebraic structure (a superhyperbolic system in our terminology) for finite quantum systems, which is a generalization of the usual one in the two-level system. It fits into the so-called generalized Pauli matrices, so they play an important role in theory. Some deep relation to the modified Bessel functions of integer order is pointed out. By taking a skillful limit finite quantum systems become quantum mechanics on the circle developed by Ohnuki and Kitakado.

Asymptotic expansions and converging factors V. Lommel, Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions

1959 ◽  
Vol 249 (1257) ◽  
pp. 284-292 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Lommel Functions ◽  
Special Cases

A theory of Lommel functions is developed, based upon the methods described in the first four papers (I to IV) of this series for replacing the divergent parts of asymptotic expansions by easily calculable series involving one or other of the four ‘basic converging factors’ which were investigated and tabulated in I. This theory is then illustrated by application to the special cases of Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions.

(p, q)-Extended Bessel and Modified Bessel Functions of the First Kind

2017 ◽  
Vol 72 (1-2) ◽  
pp. 617-632 ◽  
Author(s):  
Dragana Jankov Maširević ◽  
Rakesh K. Parmar ◽  
Tibor K. Pogány
Keyword(s):  
Bessel Functions ◽  
Modified Bessel Functions
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