2 citations · 3 across the 11 of their papers we have counts for
12 papers
A Generalization of the Riemann Functional Equation with Three Variables
José Risomar Sousa
The discovery that the generalized Riemann functional equation from the literature can be extended to real , by exploiting symmetries of a new formula for the Hurwitz zeta…
Simplest Integrals for the Zeta Function and its Generalizations Valid in All
Jose Risomar Sousa
A formula for the Riemann zeta function is obtained as an extension of the Faulhaber formula and, from there, formulae for its generalizations (the Hurwitz zeta, , the pol…
Lerch's and the Polylogarithm at the Negative Integers
Jose Risomar Sousa
At the negative integers, there is a simple relation between the Lerch function and the polylogarithm. Starting from that relation and a formula for the polylogarithm at the ne…
The Faulhaber Formula Analytic Continuation
Jose Risomar Sousa
We extend the Faulhaber formula to the whole complex plane, obtaining an expression that fully resembles the Euler-Maclaurin summation formula, only it's exact. Thereafter, an expr…
The Lerch Analytic Continuation
Jose Risomar Sousa
We demonstrate how to extend formulae for the Lerch transcendent function, , and the polylogarithm, , that only hold at the positive integers to…
A Reformulation of the Riemann Hypothesis
Jose Risomar Sousa
We present some novelties on the Riemann zeta function. Using an extended formula created for the polylogarithm in a previous paper, , the zeta function's D…
Lerch's and the Polylogarithm at the Positive Integers
Jose Risomar Sousa
We review the closed forms of the partial Fourier sums associated with $\HP_k(n)$ from a previous paper and create an asymptotic expression for $\HP(n)$ as a way to obtain formulae…
An Exact Formula for the Prime Counting Function
Jose Risomar Sousa
This paper discusses a few main topics in Number Theory, such as the Möbius function and its generalization, leading up to the derivation of neat power series for the prime countin…
The Hurwitz Zeta Function at the Positive Integers
Jose Risomar Sousa
A formula for the Hurwitz zeta function at the positive integers , , is created by solving the real and the imaginary parts separately and then combining them. A few dif…
Generalized Harmonic Progression Part II
Jose Risomar Sousa
In a previous paper, we saw how to create formulae for the sum of the terms of a harmonic progression of order , , with integer parameters, and . In thi…
Generalized Harmonic Progression
Jose Risomar Sousa
This paper presents formulae for the sum of the terms of a harmonic progression of order with integer parameters, , and for the partial sums of its two associ…
Generalized Harmonic Numbers
Jose Risomar Sousa
This paper presents new formulae for the harmonic numbers of order , , and for the partial sums of two Fourier series associated with them, denoted here by $C^m_{k}(n)…