Author:
Bansal Deepak,Raina Ravinder Krishna,Maharana Sudhananda,Cho Nak Eun
Abstract
AbstractOur purpose in the present investigation is to study certain geometric properties such as the close-to-convexity, convexity, and starlikeness of the hypergeometric function $z{}_{1}F_{2}(a;b,c;z)$
z
1
F
2
(
a
;
b
,
c
;
z
)
in the open unit disk. The usefulness of the main results for some familiar special functions like the modified Sturve function, the modified Lommel function, the modified Bessel function, and the ${}_{0}F_{1}(-;c;z)$
F
1
0
(
−
;
c
;
z
)
function are also mentioned. We further consider a boundedness property of the function $_{1}F_{2}(a;b,c;z)$
F
2
1
(
a
;
b
,
c
;
z
)
in the Hardy space of analytic functions. Several corollaries and special cases of the main results are also pointed out.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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