Construction of the lowest-order recurrence relation for the Jacobi coefficients
S. Lewanowicz (1983)
Applicationes Mathematicae
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S. Lewanowicz (1983)
Applicationes Mathematicae
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Chen, Ming-Po, Srivastava, H.M. (1995)
Journal of Applied Mathematics and Stochastic Analysis
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L. Carlitz (1967)
Rendiconti del Seminario Matematico della Università di Padova
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H. L. Manocha, H. R. Sharma (1970)
Matematički Vesnik
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Boychev, Georgi (2011)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 33C45, 40G05. In this paper we give some results concerning the equiconvergence and equisummability of series in Jacobi polynomials.
Yadav, Sarjoo Prasad (2004)
International Journal of Mathematics and Mathematical Sciences
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B. L. Sharma, H. L. Manocha (1969)
Matematički Vesnik
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Moak, Daniel S. (1984)
International Journal of Mathematics and Mathematical Sciences
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Christophe Smet, Walter Van Assche (2009)
Acta Arithmetica
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Wenchang Chu (2007)
Bollettino dell'Unione Matematica Italiana
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The simplest proof of Jacobi's triple product identity originally due to Cauchy (1843) and Gauss (1866) is reviewed. In the same spirit, we prove by means of induction principle and finite difference method, a finite form of the quintuple product identity. Similarly, the induction principle will be used to give a new proof of another algebraic identity due to Guo and Zeng (2005), which can be considered as another finite form of the quintuple product identity.
S. Lewanowicz (1987)
Applicationes Mathematicae
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Szyjewski, Marek (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 11A15. We extend to the Jacobi symbol Zolotarev's idea that the Legendre symbol is the sign of a permutation, which leads to simple, strightforward proofs of many results, the proof of the Gauss Reciprocity for Jacobi symbols including.
H. L. Manocha (1974)
Matematički Vesnik
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