Radii of Starlikeness and Convexity of a Product and Cross-Product of Bessel Functions

On some geometric properties of normalized Wright functions

“…Because of the fact that special functions play a key role in solving many problems in mathematics, applied mathematics and physics they have received a great deal of attention by many researchers from geometric function theory field (see the recent papers [1][2][3][4][5]7,9,17] and the references therein). In addition, for comprehensive knowledge on the radius problems of some special functions, one may consult on the works [6,10,13,16,18].…”

“…With the aid of [9] we know that if > 0 and > 0, then the function ↦ , ( ) = ( , , − 2 ) has infinitely many zeros which are all real. If we denote the th positive zero of the function ↦ ( , , − 2 ) by , , , under the same conditions the infinite product representation…”

Properties of the cross-product of Bessel and modified Bessel functions of the first kind

“…Therefore, whenever a, b ∈ (0, 1) ⊂ (0, j ν,1 ), they should be equal and then a = b = 2 −1/n . Now, in view of the infinite product representation (see [1,4]) of Φ ν (x) as well as of Π ν (x) = J ν (x)I ν (x) we get…”

Geometric and monotonic properties of hyper-Bessel functions

“…Recently, there has been a vivid interest on some geometric properties such as univalency, starlikeness, convexity and uniform convexity of various special functions such as Bessel, Struve, Lommel, Wright and q-Bessel functions (see [1,2,3,4,7,8,9,10,11,15,16,13,17]). In the above mentioned papers the authors have used frequently some properties of the zeros of these functions.…”