Deriving a generating function for the Riemann Zeta functional polynomial appears to be missing as there is no obvious way to proceed. Here the argument of the Zeta function is limited to Re(s) > 1.0 to make sure that the domain excludes the singularity at s = 1. A generating function for the polynomial is derived and is given in a rather simple form for further analysis.

Visilab Report #2023-08

Creating a generating function for a polynomial is sometimes very troublesome as there seems not to be a general method available. Each polynomial will usually require a specific way. A procedure is needed to ease creating a generating function for a new polynomial. A method is derived for this purpose appearing to be universal and independent of the details of the polynomial. A second method is given applying to more complex polynomial types being also universal, except for the power’s index function.

Henrik Stenlund, " On Transforming the Laplace Operator ", IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 17, Issue 3 Ser. I (May – June 2021), PP 59-64 www.iosrjournals.org 8 May 2021 (local copy)

Visilab Report #2021-05

In this communication it is shown that a function of the Laplace operator acting on an arbitrary function can be transformed to a three-dimensional integral. The cases of the exponential function and of an arbitrary function expressible as a power series, are treated. Two special cases of radial functions are presented based on elementary observations made here.

Visilab Report #2020-11

This study derives the connection between the functional power series and the inversion formula, both given in series form. The link is established by differentiation of the inversion formula showing an expression of a functional power series for the reciprocal of the derivative in terms of the function itself.

Visilab Report #2019-04

Four new relations have been found between the Stirling numbers of first and second kind. They are derived directly from recently published relations.

Henrik Stenlund, "On Studying the Phase Behavior of the Riemann Zeta Functions Along the Critical Line", arXiv:1806.011148v1 [math.GM] 1 Jun 2018 (local copy)

Visilab Report #2018-06

The critical line of the Riemann zeta function is studied from a new viewpoint. It is found that the ratio between the zeta function at any zero and the corresponding one at a conjugate point has a certain phase and its absolute value is unity. This fact is valid along the whole critical line and only there. The common functional equation is used with the aid of the function ratio between any zero and its negative side pair, a complex conjugate. As a result, an equation is obtained for solving the phase along the critical line.

DOI: 10.13140/RG.2.1.4197.1285

Visilab Report #2015-11

   - We present some results obtained for the Cauchy-Euler differential operator, especially for the exponential function of it.

Henrik Stenlund,"On Solving the Cauchy Problem with Propagators", arXiv:1411.1402v1[math.AP], 5th November 2014 (local copy)

Visilab Report #2014-11

   - The abstract first order Cauchy problem is solved in terms of Taylor’s series leading to a series of operators which is a propagator. It is found that higher order Cauchy problems can be solved in the same way. Since derivatives of order lower than the Cauchy problem are built-in to the problem, it suffices to solve the higher order derivatives in terms of the lower order ones, in a simple way.

Henrik Stenlund,"On a Method for Solving Infinite Series", arXiv:1405.7633v2[math.GM], 6th May 2014 (local copy)

Visilab Report #2014-05

   - This paper is about a method for solving infinite series in closed form by using inverse and forward Laplace transforms. The resulting integral is to be solved instead. The method is extended by parametrizing the series. A further Laplace transform with respect to it will offer more options for solving a series.

Henrik Stenlund, "A Note on Laplace Transforms of Some Particular Function Types",  arXiv:1402.2876v1[math.GM], 9th Feb 2014 (local copy)

Visilab Report #2014-02

   - This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform for its inverse when there is a specific type of an implicit function involved .

Henrik Stenlund, "On Solving Some Trigonometric Series",  arXiv:1308.2626v1[math.GM], 5th Aug 2013 (local copy)

Visilab Report #2013-08

   - This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function. We have found a new series expression for the logarithm as a side effect. The new series are useful both for analysis, approximations and asymptotic studies.