The Asymptotic Expansion of a Function Introduced by L.L. Karasheva

Richard Paris
Additional contact information
Richard Paris: Division of Computing and Mathematics, Abertay University, Dundee DD1 1HG, UK

Mathematics, 2021, vol. 9, issue 12, 1-10

Abstract: The asymptotic expansion for x ? ± ? of the entire function F n , ? ( x ; ? ) = ? k = 0 ? sin ( n ? k ) sin ? k x k k ! ? ( ? ? ? k ) , ? k = ( k + 1 ) ? 2 n for ? > 0 , 0 < ? < 1 and n = 1 , 2 , … is considered. In the special case ? = ? / ( 2 n ) , with 0 < ? < 1 , this function was recently introduced by L.L. Karasheva ( J. Math. Sciences , 250 (2020) 753–759) as a solution of a fractional-order partial differential equation. By expressing F n , ? ( x ; ? ) as a finite sum of Wright functions, we employ the standard asymptotics of integral functions of hypergeometric type to determine its asymptotic expansion. This was found to depend critically on the parameter ? (and to a lesser extent on the integer n ). Numerical results are presented to illustrate the accuracy of the different expansions obtained.

Keywords: wright function; asymptotic expansions; Stokes phenomenon (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/12/1454/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/12/1454/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:12:p:1454-:d:579176

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().