Abstract
Complete Monotonicity Properties of a Function Involving the Polygamma Function
Highlights
Introduction and PreliminariesThe classical Gamma function, which is an extension of the factorial notation to noninteger values is usually defined as ∞Γ(x) = tx−1e−t dt, x > 0, and satisfying the basic propertyΓ(x + 1) = xΓ(x), x > 0.Its logarithmic derivative, which is called the Psi or digamma function is defined as ψ(x) d dx ln Γ(x) −γ∞ 0 e−t − e−xt 1 − e−t dt, x > 0, (1)
We study completete monotonicity properties of the function fa,k(x)
In [6], Qiu and Vuorinen established among other things that the function h1 = ψ x is strictly decreasing and convex on (0, ∞)
Summary
We study completete monotonicity properties of the function fa,k(x) We deduce some inequalities involving the polygamma functions. Its logarithmic derivative, which is called the Psi or digamma function is defined as ∞ 0 tne−xt 1 − e−t dt, x > 0, (2) X > 0, k=0 satisfying the functional equation [1, p.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
