Abstract
Logarithmic derivative of the multiple gamma function is known as the multiple psi function. In this work q-analogue of multiple psi functions of order n have been considered. Subadditive, superadditive and convexity properties of higher order derivatives of these functions are derived. Some related inequalities for these functions and their ratios are also obtained.
Highlights
The multiple gamma functions of Barnes [4, 5] introduced more than a century ago have been taken up during the last decades because they enter in several different areas of modern mathematics represented by e.g., S
Multiple gamma functions Γn are useful to study the determinant of Laplacians on the ndimensional unit sphere Sn [7]
Logarithmic derivative of the multiple gamma function is known as the multiple psi function and is denoted by
Summary
The multiple gamma functions of Barnes [4, 5] introduced more than a century ago have been taken up during the last decades because they enter in several different areas of modern mathematics represented by e.g., S. The multiple gamma functions Γn (n ∈ N) which are defined and denoted by Gn := Γn(−1)n−1 satisfy the following recurrence relation (−1)n d n+1 d xn+1 log Γn(x) are known as the conditions of generalized Bohr–Mollerup theorem. The poly multiple gamma function Ψ(nm) is the m-th order derivative of Ψn.
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