Univalence of Bessel Functions

نویسنده

  • R. K. BROWN
چکیده

In particular we shall first determine a radius of univalence for the normalized Bessel functions [7>(z)]1/" for values of v belonging to the region G defined by the inequalities 6{\v} >0, | arg »»| <7r/4. Then we shall determine the radius of univalence of the functions z1_"7,.(z) for values of v belonging to a subset of the closure of G. When v is real and positive we shall determine the exact radius of star-likeness of both of the above-mentioned classes of normalized Bessel functions. Our results concerning the functions z1~"Jv(z) "sharpen" those of Kreyszig and Todd [l] when v — 0 and extend their results for complex values of v. 2. Preliminaries. Let

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تاریخ انتشار 2010