Convergent Factorial Series Expansions for Bessel Functions

1991 ◽  
Vol 22 (4) ◽  
pp. 1156-1172 ◽  
Author(s):  
T. M. Dunster ◽  
D. A. Lutz
Keyword(s):  
Bessel Functions ◽  
Series Expansions ◽  
Factorial Series

scholarly journals A note on generalized factorial series expansions

1977 ◽  
Vol 7 (2) ◽  
pp. 605-628 ◽  
Author(s):  
Mitsuhiko Kohno ◽  
Masahide Ohtomo
Keyword(s):  
Series Expansions ◽  
Factorial Series

Convergent Liouville–Green expansions for second-order linear differential equations, with an application to Bessel functions

1993 ◽  
Vol 440 (1908) ◽  
pp. 37-54 ◽  
Keyword(s):  
Differential Equations ◽  
Bessel Functions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Large Parameter ◽  
Order Linear ◽  
Factorial Series ◽  
Independent Variable ◽  
Linear Differential ◽  
Asymptotic Validity

A class of second-order linear differential equations with a large parameter u is considered. It is shown that Liouville–Green type expansions for solutions can be expressed using factorial series in the parameter, and that such expansions converge for Re ( u ) > 0, uniformly for the independent variable lying in a certain subdomain of the domain of asymptotic validity. The theory is then applied to obtain convergent expansions for modified Bessel functions of large order.

SERIES EXPANSIONS OF THE GENERALIZED K-BESSEL FUNCTIONS ON SYMMETRIC CONES

2008 ◽  
Vol 06 (01) ◽  
pp. 1-10 ◽  
Author(s):  
HONGMING DING ◽  
WEI HE
Keyword(s):  
Series Expansion ◽  
Bessel Functions ◽  
Series Expansions ◽  
Symmetric Cones ◽  
Expansion Formula

In this paper, we generalize the series expansion formula of classical K-Bessel functions to symmetric cones.

scholarly journals Integrals and series related to propagators of neural and haemodynamic waves

2021 ◽  
Vol 8 (12) ◽  
Author(s):  
P. A. Robinson
Keyword(s):  
Green Function ◽  
Neural Activity ◽  
Bessel Functions ◽  
Series Expansions

The propagator, or Green function, of a class of neural activity fields and of haemodynamic waves is evaluated exactly. The results enable a number of related integrals to be evaluated, along with series expansions of key results in terms of Bessel functions of the second kind. Connections to other related equations are also noted.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

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