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On a q ‐Laplace–type integral operator and certain class of series expansion
Author(s) -
AlOmari S. K. Q.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6002
Subject(s) - mathematics , bessel function , laplace transform , type (biology) , series (stratigraphy) , hypergeometric function , operator (biology) , power series , special functions , pure mathematics , trigonometric functions , mathematical analysis , algebra over a field , ecology , paleontology , biochemistry , chemistry , geometry , repressor , gene , transcription factor , biology
In this paper, we develop a q ‐theory of the q ‐Laplace–type integral operators q L 2 and q l 2 introduced by Uçar and Albayrak in 2011. We derive several identities and establish various results related to the q ‐Laplace–type integral operators of various classes of q ‐special functions and q ‐series expansions. By using a q ‐series representation of the q ‐analogues, we obtain results enfolding power series of even orders. Further, by utilizing the new results, we obtain formulas and conclusions associated with q ‐hypergeometric functions of first and second types. In a brief reading, we finally establish new formulas involving q ‐trigonometric and q ‐Bessel functions as well.