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Old and New Identities for Bernoulli Polynomials via Fourier Series
Joint Authors
Navas, Luis M.
Varona, Juan L.
Ruiz, Francisco J.
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-12
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
The Bernoulli polynomials Bk restricted to [0,1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk.
In general, the Fourier coefficients of any polynomial restricted to [0,1) are linear combinations of terms of the form 1/nk.
If we can make this linear combination explicit for a specific family of polynomials, then by uniqueness of Fourier series, we get a relation between the given family and the Bernoulli polynomials.
Using this idea, we give new and simpler proofs of some known identities involving Bernoulli, Euler, and Legendre polynomials.
The method can also be applied to certain families of Gegenbauer polynomials.
As a result, we obtain new identities for Bernoulli polynomials and Bernoulli numbers.
American Psychological Association (APA)
Navas, Luis M.& Ruiz, Francisco J.& Varona, Juan L.. 2012. Old and New Identities for Bernoulli Polynomials via Fourier Series. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-447956
Modern Language Association (MLA)
Navas, Luis M.…[et al.]. Old and New Identities for Bernoulli Polynomials via Fourier Series. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-14.
https://search.emarefa.net/detail/BIM-447956
American Medical Association (AMA)
Navas, Luis M.& Ruiz, Francisco J.& Varona, Juan L.. Old and New Identities for Bernoulli Polynomials via Fourier Series. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-447956
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447956