Series Involving the Zeta Functions and a Family of Generalized Goldbach–Euler Series

Abstract

We first present the corrected expression for a certain widely-recorded generalized Goldbach–Euler series. The corrected forms are then shown to be connected with the problem of closed-form evaluation of series involving the Zeta functions, which happens to be an extensively-investigated subject since the time of Euler as (for example) in the classical three-century-old Goldbach theorem.

Additional information

Notes on contributors

Junesang Choi

JUNESANG CHOI received his B.S. and M.S. from Gyeongsang National University (Republic of Korea) in 1981 and 1983, respectively, and his Ph.D. from the Florida State University in 1991. He currently teaches at Dongguk University (Gyeongju) in the Republic of Korea. His publications include 137 papers and 4 books. See http://wwwk.dongguk.ac.kr/~junesang/.

Hari M. Srivastava

HARI M. SRIVASTAVA is Professor Emeritus at the University of Victoria since 2006, having joined the faculty there in 1969. He has held other faculty positions and visiting positions at many universities and research institutes around the world. He has written more than 1000 papers and has collaborated with over 400 co-authors. His other publications include (for example) 21 books, monographs, and edited volumes. See http://www.math.uvic.ca/faculty/harimsri/.