A MONOTONICITY PROPERTY INVOLVING THE GENERALIZED ELLIPTIC INTEGRAL OF THE FIRST KIND

作者：Yang, Zhen-Hang^*; Chu, Yu-Ming

来源：Mathematical Inequalities & Applications, 2017, 20(3): 729-735.

DOI：10.7153/mia-20-46

• Gaussian hypergeometric function
• generalized elliptic integral
• gamma function
• psi function
• monotonicity

In this paper, we prove that the function @@@ r -> Y(r) = Ka(r) sin(pi a)r'(2)log(e(R(a)/2)/r') - 1/r'(2) @@@ is strictly increasing from (0,1) onto (p/[R(a) sin(pi a)]-1, a(1-a)) for all a is an element of (0,1/2], where r' = root 1- r(2), K-a(r) is the generalized elliptic integral of the first kind, R(a) = -2 gamma -psi(a)-psi(1-a),. is the classical psi function and gamma = 0.57721566 . . . is the Euler-Mascheroni constant.

• 出版日期2017-7