An inequality for the q-Polygamma function

2013 ◽  
Vol 7 ◽  
pp. 693-696
Author(s):  
Banyat Sroysang
Keyword(s):  
Polygamma Function

On the matrix versions of q-zeta function, q-digamma function and q-polygamma function

2019 ◽  
Vol 13 (08) ◽  
pp. 2050142
Author(s):  
Ravi Dwivedi ◽  
Vivek Sahai
Keyword(s):  
Zeta Function ◽  
Matrix Function ◽  
Integral Representations ◽  
Digamma Function ◽  
Polygamma Function ◽  
The Matrix ◽  
Matrix Series ◽  
Zeta Matrix

This paper deals with the [Formula: see text]-analogues of generalized zeta matrix function, digamma matrix function and polygamma matrix function. We also discuss their regions of convergence, integral representations and matrix relations obeyed by them. We also give a few identities involving digamma matrix function and [Formula: see text]-hypergeometric matrix series.

Completely monotonic functions related to the q-gamma and the q-trigamma functions

2015 ◽  
Vol 13 (02) ◽  
pp. 125-134 ◽  
Author(s):  
Ahmed Salem
Keyword(s):  
Gamma Function ◽  
Infinite Class ◽  
Positive Real ◽  
Digamma Function ◽  
Sharp Bounds ◽  
Monotonic Functions ◽  
Polygamma Function ◽  
Completely Monotonic ◽  
Completely Monotonic Functions

In this paper, two completely monotonic functions involving the q-gamma and the q-trigamma functions where q is a positive real, are introduced and exploited to derive sharp bounds for the q-gamma function in terms of the q-trigamma function. These results, when letting q → 1, are shown to be new. Also, sharp bounds for the q-digamma function in terms of the q-tetragamma function are derived. Furthermore, an infinite class of inequalities for the q-polygamma function is established.

scholarly journals THE q-DEFORMED GAMMA FUNCTION AND q-DEFORMED POLYGAMMA FUNCTION

2014 ◽  
Vol 51 (4) ◽  
pp. 1155-1161 ◽  
Author(s):  
Won Sang Chung ◽  
Taekyun Kim ◽  
Toufik Mansour
Keyword(s):  
Gamma Function ◽  
Polygamma Function

scholarly journals Sharp Inequalities for Polygamma Functions

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Bai-Ni Guo ◽  
Feng Qi ◽  
Jiao-Lian Zhao ◽  
Qiu-Ming Luo
Keyword(s):  
Rational Functions ◽  
Complete Monotonicity ◽  
Double Inequality ◽  
Polygamma Function ◽  
Polygamma Functions

AbstractIn the paper, the authors review some inequalities and the (logarithmically) complete monotonicity concerning the gamma and polygamma functions and, more importantly, present a sharp double inequality for bounding the polygamma function by rational functions.

scholarly journals Bicomplex Polygamma Function

2007 ◽  
Vol 30 (2) ◽  
pp. 523-530 ◽  
Author(s):  
Ritu GOYAL
Keyword(s):  
Polygamma Function

scholarly journals A procedure for generating infinite series identities

2004 ◽  
Vol 2004 (67) ◽  
pp. 3653-3662
Author(s):  
Anthony A. Ruffa
Keyword(s):  
Zeta Function ◽  
Hypergeometric Function ◽  
Infinite Series ◽  
Special Functions ◽  
Hurwitz Zeta Function ◽  
Gauss Hypergeometric Function ◽  
Polygamma Function ◽  
Polygamma Functions ◽  
Infinite Sums ◽  
Lerch Transcendent

A procedure for generating infinite series identities makes use of the generalized method of exhaustion by analytically evaluating the inner series of the resulting double summation. Identities are generated involving both elementary and special functions. Infinite sums of special functions include those of the gamma and polygamma functions, the Hurwitz Zeta function, the polygamma function, the Gauss hypergeometric function, and the Lerch transcendent. The procedure can be automated withMathematica(or equivalent software).

SPECIAL VALUES OF THE POLYGAMMA FUNCTIONS

2009 ◽  
Vol 05 (02) ◽  
pp. 257-270 ◽  
Author(s):  
M. RAM MURTY ◽  
N. SARADHA
Keyword(s):  
Natural Number ◽  
Dirichlet Series ◽  
Linear Independence ◽  
Polygamma Function ◽  
Special Values ◽  
Polygamma Functions ◽  
Dirichlet Characters ◽  
Special Value

Let q be a natural number and [Formula: see text]. We consider the Dirichlet series ∑n ≥ 1 f(n)/ns and relate its value when s is a natural number, to the special values of the polygamma function. For certain types of functions f, we evaluate the special value explicitly and use this to study linear independence over ℚ of L(k,χ) as χ ranges over Dirichlet characters mod q which have the same parity as k.

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