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Partial fraction decompositions and trigonometric sum identities
Author:
Wenchang Chu
Journal:
Proc. Amer. Math. Soc. 136 (2008), 229-237
MSC (2000):
Primary 42A15; Secondary 65T40
Posted:
October 18, 2007
MathSciNet review:
2350408
Full-text PDF
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Additional Information
Abstract: The partial fraction decomposition method is explored to establish several interesting trigonometric function identities, which may have applications to the evaluation of classical multiple hypergeometric series, trigonometric approximation and interpolation.
- 1.
Bruce
C. Berndt and Boon
Pin Yeap, Explicit evaluations and reciprocity theorems for finite
trigonometric sums, Adv. in Appl. Math. 29 (2002),
no. 3, 358–385. MR 1942629
(2003h:11092), http://dx.doi.org/10.1016/S0196-8858(02)00020-9
- 2.
Francesco
Calogero, Classical many-body problems amenable to exact
treatments, Lecture Notes in Physics. New Series m: Monographs,
vol. 66, Springer-Verlag, Berlin, 2001. (Solvable and/or integrable
and/or linearizable...) in one-, two- and three-dimensional space. MR 1880249
(2003a:37074)
- 3.
Wen-Chang
Chu, Summations on trigonometric functions, Appl. Math.
Comput. 141 (2003), no. 1, 161–176. Advanced
special functions and related topics in differential equations (Melfi,
2001). MR
1986078 (2004h:33003), http://dx.doi.org/10.1016/S0096-3003(02)00330-2
- 4.
Wenchang
Chu and Alberto
Marini, Partial fractions and trigonometric identities, Adv.
in Appl. Math. 23 (1999), no. 2, 115–175. MR 1699235
(2000i:33001), http://dx.doi.org/10.1006/aama.1998.0635
- 5.
W. Chu, X. X. Wang, D. Y. Zheng, Application of the residue theorem to bilateral hypergeometric series Preprint, 2006.
- 6.
M. A. Dougall, On Vandermonde's theorem and some more general expansion Proc. Edinburgh. Math. Soc.25 (1907), 114-132.
- 7.
Ira
M. Gessel, Generating functions and generalized Dedekind sums,
Electron. J. Combin. 4 (1997), no. 2, Research Paper
11, approx. 17 pp. (electronic). The Wilf Festschrift (Philadelphia, PA,
1996). MR
1444158 (98f:11032)
- 8.
R.
A. Gustafson, Multilateral summation theorems for ordinary and
basic hypergeometric series in 𝑈(𝑛), SIAM J. Math.
Anal. 18 (1987), no. 6, 1576–1596. MR 911651
(90e:33015), http://dx.doi.org/10.1137/0518114
- 9.
Robert
A. Gustafson, Some 𝑞-beta and Mellin-Barnes
integrals on compact Lie groups and Lie algebras, Trans. Amer. Math. Soc. 341 (1994), no. 1, 69–119. MR 1139492
(94c:33032), http://dx.doi.org/10.1090/S0002-9947-1994-1139492-3
- 10.
Rainer
Kress, Numerical analysis, Graduate Texts in Mathematics,
vol. 181, Springer-Verlag, New York, 1998. MR 1621952
(99c:65001)
- 11.
Martin
J. Mohlenkamp and Lucas
Monzón, Trigonometric identities and sums of separable
functions, Math. Intelligencer 27 (2005), no. 2,
65–69. MR
2156535, http://dx.doi.org/10.1007/BF02985795
- 1.
- B. C. Berndt, Explicit evaluations and reciprocity theorems for finite trigonometric sums Advances in Appl. Math.29 (2002), 358-385. MR 1942629 (2003h:11092)
- 2.
- F. Calogero, Classical Many-Body Problems Amenable to Exact Treatments Lecture Notes in Physics: M66, Springer-Verlag (2001), Berlin. MR 1880249 (2003a:37074)
- 3.
- W. Chu, Summations on trigonometric functions Applied Mathematics and Computation 141 (2003), 161-176. MR 1986078 (2004h:33003)
- 4.
- W. Chu, A. Marini, Partial fractions and trigonometric identities Advances in Appl. Math.23 (1999), 115-175. MR 1699235 (2000i:33001)
- 5.
- W. Chu, X. X. Wang, D. Y. Zheng, Application of the residue theorem to bilateral hypergeometric series Preprint, 2006.
- 6.
- M. A. Dougall, On Vandermonde's theorem and some more general expansion Proc. Edinburgh. Math. Soc.25 (1907), 114-132.
- 7.
- I. M. Gessel, Generating functions and generalized Dedekind sums Elec. J. Combin.4 (1997), #R11. MR 1444158 (98f:11032)
- 8.
- R. A. Gustafson, Multilateral summation theorems for ordinary and basic hypergeometric series in
 SIAM J. Math. Anal.18 (1987), 1576-1596. MR 911651 (90e:33015)
- 9.
- R. A. Gustafson, Some q-beta and Mellin-Barnes integrals on compact Lie groups and Lie algebras Trans. Amer. Math. Soc.341 (1994), 69-119. MR 1139492 (94c:33032)
- 10.
- R. Kress, Numerical Analysis: Graduate Texts in Mathematics (GTM181) Springer-Verlag (1998), Berlin-Heidelberg. MR 1621952 (99c:65001)
- 11.
- M. J. Mohlenkamp, L. Monzón, Trigonometric identities and sums of separable functions The Mathematical Intelligencer 27:2 (2005), 65-69. MR 2156535
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Additional Information
Wenchang Chu
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, People’s Republic of China
Address at time of publication:
Dipartimento di Matematica, Universit\a‘a degli Studi di Lecce, Lecce-Arne- sano, P. O. Box 193, 73100 Lecce, Italia
Email:
chu.wenchang@unile.it
DOI:
http://dx.doi.org/10.1090/S0002-9939-07-09085-5
PII:
S 0002-9939(07)09085-5
Keywords:
Trigonometric interpolation,
trigonometric formulae,
partial fraction decomposition.
Received by editor(s):
October 25, 2006
Posted:
October 18, 2007
Communicated by:
Carmen C. Chicone
Article copyright:
© Copyright 2007 American Mathematical Society
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