8 papers
A Table of Generating Functions
Robert Reynolds
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand fun…
Extended Blumberg-Dieckmann Series
Robert Reynolds
This paper introduces a set of finite summation formulas and utilize them to establish various functional relationships involving the multivariable Hurwitz-Lerch zeta function. Add…
Finite Sums and Products involving Special Functions
Robert Reynolds
Various product and sum relationships are established using special functions, specifically involving Special functions. These relationships are derived from formulas inspired by t…
Double Sum involving Product of Appell-Type Bernoulli and Euler Polynomials
Robert Reynolds
In this work we derive a bilateral generating function involving the product of an Appell-type product of the Bernoulli and Euler polynomials over independent indices and orders. T…
Extended Watson-Harkins Sum
Robert Reynolds
The Watson-Harkins sum involving the product of the cosine and cosecant functions is extended to derive the finite sum of generalized Hurwitz-Lerch Zeta functions is derived in ter…
Special Function Representation Of Dickson Polynomials
Robert Reynolds
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of t…
Sum of the Hurwitz-Lerch Zeta Function over Prime Numbers: Derivation and Evaluation
Robert Reynolds, Allan Stauffer
For the function , where general complex numbers and any positive integer, we establish the sum of values of the Hurwitz-Lerch zeta function $Φ(f(m,p,q,n),k…
Definite integrals involving combinations of powers and logarithmic functions of complicated arguments expressed in terms of the Hurwitz zeta function
Robert Reynolds, Allan Stauffer
In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integral…