Functional Equations related to the Dirichlet lambda and beta functions

2014/04/22 by JeonWon Kim, Kim, JeonWon
Mathematics · #11M41 #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1404.5467

openalex publication_date 2014/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give closed-form expressions for the Dirichlet beta function at even positive integers and for the Dirichlet lambda function at odd positive integers, based on the function J(s) defined via convergent integral. We also show fundamental relations between Dirichlet lambda and beta functions and the function J(s).

Related

• Fundamental relations between the Dirichlet beta function, euler numbers, and Riemann zeta function for positive integers
• Some applications of the Beta function
• Note on extensions of the beta function
• Strong q-analogues for values of the Dirichlet beta function
• The Riemann Hypothesis for Dirichlet L Functions