A New Functional Identity for Riemann’s Zeta Function
نویسنده
چکیده
Abstract. In this short paper we present a simple method for deriving a new and remarkable functional identity for Riemann’s Zeta Function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work ”Remarques sur un beau rapport entre les series des puissances tant directes que reciproques (E 352)” in Memoires de l’Academie des Sciences de Berlin 17, (1768) permit to define a new special function, named A (s), which is fully symmetric and is similar to Riemann’s ξ function. Using the A (s) function, we obtain a new functional equation, that represents an entire function. To be complete we find also several integral representations of the A (s) function.
منابع مشابه
A Remarkable Functional Identity for Riemann’s Zeta Function
Abstract. In this short paper we present a simple method for deriving a remarkable functional identity for Riemann’s Zeta Function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work ”Remarques sur un beau rapport entre les series des puissances tant directes que reciproques (E 352)” in Memoires de l’Academie des Sciences de Berlin 17, (1768) per...
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