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Generalized Ramanujan Primes Read chapter Read first chapter

2014 | OriginalPaper | Chapter

On Sums Related to Central Binomial and Trinomial Coefficients

Author : Zhi-Wei Sun

Published in: Combinatorial and Additive Number Theory

Publisher: Springer New York

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Abstract

A generalized central trinomial coefficient T n (b, c) is the coefficient of x n in the expansion of \((x^{2} + bx + c)^{n}\) with \(b,c \in \mathbb{Z}\). In this paper we investigate congruences and series for sums of terms related to central binomial coefficients and generalized central trinomial coefficients. The paper contains many conjectures on congruences related to representations of primes by certain binary quadratic forms, and 62 proposed new series for 1∕π motivated by congruences and related dualities.

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previous chapter Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-Non-Wilson Primes 2, 3, 14771
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Metadata
Title
On Sums Related to Central Binomial and Trinomial Coefficients
Author
Zhi-Wei Sun
Copyright Year
2014
Publisher
Springer New York
Book
Combinatorial and Additive Number Theory

Print ISBN: 978-1-4939-1600-9

Electronic ISBN: 978-1-4939-1601-6

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4939-1601-6_18

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