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An elementary proof of Euler’s product expansion for the sine
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Sumit Kumar Jha
Published/Copyright:
November 23, 2019
Abstract
We give a proof of the Euler’s infinite product for the sine using elementary trigonometric identities, and Tannery’s theorem for infinite products.
References
[1] Ó. Ciaurri, Euler’s product expansion for the sine: An elementary proof, Amer. Math. Monthly 122 (2015), no. 7, 693–695. 10.4169/amer.math.monthly.122.7.693Search in Google Scholar
[2] P. Loya, Real Analysis 1, lecture notes 2005, http://people.math.binghamton.edu/dikran/478/Ch6.pdf, p. 322. Search in Google Scholar
Received: 2019-05-28
Accepted: 2019-09-27
Published Online: 2019-11-23
Published in Print: 2019-12-01
© 2019 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Global existence theory for fractional differential equations: New advances via continuation methods for contractive maps
- On rough convergence of ρ-Cauchy sequence of triple sequences
- On the affirmative solution to Salem’s problem
- An elementary proof of Euler’s product expansion for the sine
Keywords for this article
Infinite product for the sine;
Tannery’s theorem;
Wallis’s formula
identities
Articles in the same Issue
- Frontmatter
- Global existence theory for fractional differential equations: New advances via continuation methods for contractive maps
- On rough convergence of ρ-Cauchy sequence of triple sequences
- On the affirmative solution to Salem’s problem
- An elementary proof of Euler’s product expansion for the sine
