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This research focuses on extending the Hurwitz transform to a larger region and the complex plane.

January 14, 2026Open Access

Analytic Continuation of the Hurwitz Transform

Key Points

This research focuses on extending the Hurwitz transform to a larger region and the complex plane.
Analyzed conditions for meromorphic continuation of the Hurwitz transform.
Derived integral representations for the extended Hurwitz transform.
Investigated new integral identities involving the Hurwitz zeta function.
Identified sufficient conditions for meromorphic extension of the Hurwitz transform.
Provided integral representations for the extension.
Established new integral identities related to the Hurwitz zeta function.

Abstract

An integral over the unit interval of the product of a given function and the Hurwitz zeta function is known as the Hurwitz transform of the function. We give sufficient conditions on the function for the Hurwitz transform to continue meromorphically to a larger region and to the complex plane. Integral representations for the meromorphic extension of the Hurwitz transform are given, and some new integral identities involving the Hurwitz zeta function are derived.

Analytic Continuation of the Hurwitz Transform

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Abstract

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