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An Approach to the Recursive Formula of Riemann Zeta Function at Even Natural Numbers
- 1 Woodland Christian High School, Breslau, Kitchener, ON. N0B 1M0, Canada
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Abstract
This paper aims to derive a recursive relationship of the values of Riemann zeta function at even natural numbers by using the principles of elementary symmetric polynomials, and associations between them and zeta functions, thereby expressing in only terms of previous zeta function’s values. Moreover, this recursive formula is going to be proven equivalently to the explicit formula of
Keywords
Bernoulli numbers, Riemann zeta function, recursive formula
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[6]. Pascal Sebah and Xavier Gourdon, “Introduction on Bernoulli numbers” (2002)
[7]. https://en.wikipedia.org/wiki/Elementary_symmetric_polynomial
Cite this article
Chen,Y. (2025). An Approach to the Recursive Formula of Riemann Zeta Function at Even Natural Numbers. Theoretical and Natural Science,108,48-56.
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Volume title: Proceedings of the 4th International Conference on Computing Innovation and Applied Physics
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