scholarly journals On special Riemann xi function formulae of Hardy involving the digamma function

2021 ◽  
Vol 87 (12) ◽  
pp. 225-232
Author(s):  
Alexander E. Patkowski
Keyword(s):  
Digamma Function

scholarly journals New fractional approaches for n-polynomial P-convexity with applications in special function theory

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Bo Chen ◽  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Special Functions ◽  
Real Life ◽  
Fractional Integrals ◽  
Digamma Function ◽  
Novel Approach ◽  
Inequality Theory ◽  
New Strategy ◽  
Significant Mechanism

Abstract Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues with high proficiency. This manuscript contributes to a captivating association of fractional calculus, special functions and convex functions. The authors develop a novel approach for investigating a new class of convex functions which is known as an n-polynomial $\mathcal{P}$ P -convex function. Meanwhile, considering two identities via generalized fractional integrals, provide several generalizations of the Hermite–Hadamard and Ostrowski type inequalities by employing the better approaches of Hölder and power-mean inequalities. By this new strategy, using the concept of n-polynomial $\mathcal{P}$ P -convexity we can evaluate several other classes of n-polynomial harmonically convex, n-polynomial convex, classical harmonically convex and classical convex functions as particular cases. In order to investigate the efficiency and supremacy of the suggested scheme regarding the fractional calculus, special functions and n-polynomial $\mathcal{P}$ P -convexity, we present two applications for the modified Bessel function and $\mathfrak{q}$ q -digamma function. Finally, these outcomes can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem.

scholarly journals Some combinatorial series identities associated with the Digamma function and harmonic numbers

2000 ◽  
Vol 13 (3) ◽  
pp. 101-106 ◽  
Author(s):  
Tsu-Chen Wu ◽  
Shih-Tong Tu ◽  
H.M. Srivastava
Keyword(s):  
Harmonic Numbers ◽  
Digamma Function

scholarly journals Some extensions of the Prabhu-Srivastava theorem involving the (p,q)-gamma function

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4507-4513
Author(s):  
Ji-Cai Liu ◽  
Jichun Liu
Keyword(s):  
Gamma Function ◽  
Digamma Function ◽  
Derivatives Of

In this paper, we obtain some limit formulas for derivatives of (p,q)-gamma function and (p,q)- digamma function at their poles. These limit formulas extend the Prabhu-Srivastava theorem involving gamma function and digamma function.

Exact Frequency Equation of a Linear Structure Carrying Lumped Elements Using the Assumed Modes Method

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Philip D. Cha ◽  
Siyi Hu
Keyword(s):  
Linear Structure ◽  
Frequency Equation ◽  
Governing Equations ◽  
Linear Structures ◽  
Combined System ◽  
Digamma Function ◽  
Simply Supported ◽  
Lumped Elements ◽  
Finite Sum ◽  
Infinite Sum

Combined systems consisting of linear structures carrying lumped attachments have received considerable attention over the years. In this paper, the assumed modes method is first used to formulate the governing equations of the combined system, and the corresponding generalized eigenvalue problem is then manipulated into a frequency equation. As the number of modes used in the assumed modes method increases, the approximate eigenvalues converge to the exact solutions. Interestingly, under certain conditions, as the number of component modes goes to infinity, the infinite sum term in the frequency equation can be reduced to a finite sum using digamma function. The conditions that must be met in order to reduce an infinite sum to a finite sum are specified, and the closed-form expressions for the infinite sum are derived for certain linear structures. Knowing these expressions allows one to easily formulate the exact frequency equations of various combined systems, including a uniform fixed–fixed or fixed-free rod carrying lumped translational elements, a simply supported beam carrying any combination of lumped translational and torsional attachments, or a cantilever beam carrying lumped translational and/or torsional elements at the beam's tip. The scheme developed in this paper is easy to implement and simple to code. More importantly, numerical experiments show that the eigenvalues obtained using the proposed method match those found by solving a boundary value problem.

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.

Some results on the digamma function

2013 ◽  
Vol 7 (1) ◽  
pp. 167-170 ◽  
Author(s):  
Biljana Tuneska ◽  
Ilija Jolevski
Keyword(s):  
Digamma Function

scholarly journals Some series whose coefficients involve the valueζ(n)for $n$nodd

1989 ◽  
Vol 12 (3) ◽  
pp. 583-587
Author(s):  
L. R. Bragg
Keyword(s):  
Wave Equation ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Digamma Function ◽  
Representation Of Solutions ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Underlying Variable

By using two basic formulas for the digamma function, we derive a variety of series that involve as coefficients the values(2n+1),n=1,2,⋯,of the Riemann-zeta function. A number of these have a combinatorial flavor which we also express in a trignometric form for special choices of the underlying variable. We briefly touch upon their use in the representation of solutions of the wave equation.

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 Analytic computation of digamma function using some new identities

2020 ◽  
Vol 16 (1) ◽  
pp. 5-12
Author(s):  
M. I. Qureshi ◽  
M. Shadab
Keyword(s):  
Gamma Function ◽  
Digamma Function ◽  
Analogous Manner ◽  
Fractional Orders ◽  
Analytic Computation

AbstractMotivated by the substantial development in the theory of digamma function, we derive some new identities for the digamma function. These new identities enable us to compute the values of the digamma function for fractional orders in an analogous manner. Also, we mention two errata, found in Jensen’s article (An elementary exposition of the theory of the Gamma function, 1916), and present their correct forms.

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