Lemniscate Convexity and Other Properties of Generalized Bessel Functions

Sufficient conditions on associated parameters p,b and c are obtained so that the generalized and \textquotedblleft{normalized}\textquotedblright{} Bessel function u_p(z)=u_{p,b,c}(z) satisfies |(1+(zu''_p(z)/u'_p(z)))^2-1|<1 or |((zu_p(z))'/u_p(z))^2-1|<1. We also determine the condition on these parameters so that -(4(p+(b+1)/2)/c)u'_p(z)\prec\sqrt{1+z}. Relations between the parameters \mu and p are obtained such that the normalized Lommel function of... Show more