39 citations · 95 across the 21 of their papers we have counts for
17 papers · 1 filter
Determining the Indeterminate: On the Evaluation of Integrals that connect Riemann's, Hurwitz' and Dirichlet's Zeta, Eta and Beta functions
Michael Milgram
By applying the inverse Mellin transform to some simple closed form identities, a number of relationships are established that connect integrals containing Riemann's and Hurwitz' z…
A Series Representation for Riemann's Zeta Function and some Interesting Identities that Follow
Michael Milgram
Using Cauchy's Integral Theorem as a basis, what may be a new series representation for Dirichlet's function , and hence Riemann's function , is obtained in terms of th…
Some Additions to a Family of Sums and Integrals related to Hurwitz' Zeta Function(s), Euler polynomials and Euler Numbers
Michael Milgram
Integrals involving the kernel function over a semi-infinite range are of general interest in the study of Riemann's function and Hurwitz' function . Suc…
An Integral Equation for Riemann's Zeta Function and its Approximate Solution
Michael Milgram
Two identities extracted from the literature are coupled to obtain an integral equation for Riemann's function, and thus indirectly. The equation has a number of simp…
Variations on a Hypergeometric Theme
Michael Milgram
The question was asked: Is it possible to express the function \begin{equation} \tag{1.1} h(a)\equiv\,{_4F_3}(a,a,a,a;2a,a+1,a+1;1) \label{question} \end{equation} in closed form?…
Further Exploration of Riemann's Functional Equation
Michael Milgram
A previous exploration of the Riemann functional equation that focussed on the critical line, is extended over the complex plane. Significant results include a simpler derivation o…