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Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 4

Trigonometric expressions for Gaussian ${}_2F_1$ -series

Wenchang CHU
Sayfa
1823–1836
Yayın Tarihi
2022-11-04
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Several closed formulae are derived in terms of trigonometric functions.Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating 3F2 -series.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The classical Gaussian 2F1 -series containing two free variables fx; yg and two integer parameters fm; ngare investigated by the linearization method.
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Temel Bulgular & Veri:The classical Gaussian 2F1 -series containing two free variables fx; yg and two integer parameters fm; ngare investigated by the linearization method.
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Sonuç & Katkı:Several closed formulae are derived in terms of trigonometric functions.Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating 3F2 -series.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

The classical Gaussian 2F1 -series containing two free variables fx; yg and two integer parameters fm; ngare investigated by the linearization method. Several closed formulae are derived in terms of trigonometric functions.Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating 3F2 -series.

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Bu Makaleye Atıf Yap

CHU, W. (2022). Trigonometric expressions for Gaussian ${}_2F_1$ -series. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 1823–1836. https://ajindex.com/articles/607644

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Kaynakça (19)

  1. Bailey WN. Generalized Hypergeometric Series. Cambridge, UK: Cambridge University Press, 1935
  2. Chen X, Chu W. The Pfaff–Saalsch theorem and terminating 3F2( 4 3 ) series. Journal of Mathematical Analysis and Applications 2011; 380 (2): 440-454
  3. Chen X, Chu W. Closed formulae for a class of terminating 3F2(4) -series. Integral Transforms and Special Functions 2017; 28 (11): 825-837
  4. Chen X, Chu W. Terminating 3F2(4) -series extended with three integer parameters. Journal of Difference Equations and Applications 2018; 24 (8): 1346-1367
  5. Chu W. Inversion techniques and combinatorial identities. Bollettino dell’Unione Matematica Italiana 1993; B7: 737-760
  6. Chu W. Inversion techniques and combinatorial identities: a quick introduction to hypergeometric evaluations. Applied Mathematics 1994; 283: 31-57
  7. Chu W. Summations on trigonometric functions. Applied Mathematics and Computation 2003; 141: 161-176
  8. Chu W. Analytical formulae for extended 3F2 -series of Watson–Whipple–Dixon with two extra integer parameters. Mathematics of Computation 2012; 81 (277): 467-479
  9. Chu W. Terminating 4F3 -series extended with two integer parameters. Integral Transforms and Special Functions 2016; 27 (10): 794-805
  10. Chu W. Terminating 2F1(4) -series perturbed by two integer parameters. Proceedings of the American Mathematical Society 2017; 145 (3): 1031-1040
  11. Chu W. Evaluation of nonterminating 3F2( 3 4 ) -series. Journal of Mathematical Analysis and Applications 2017; 450 (1): 490-503
  12. Chu W. Hypergeometric approach to Apery-like series. Integral Transforms and Special Functions 2017; 28 (7): 505-518
  13. Chu W, Zheng DY. Infinite series with harmonic numbers and central binomial coefficients. International Journal of Number Theory 2009; 5 (3): 429-448
  14. Gould HW, Hsu LC. Some new inverse series relations. Duke Mathematical Journal 1973; 40: 885-891
  15. Gradshteyn IS, Ryzhik IM. Table of Integrals, Series and Products (Sixth Edition). Singapore: Elsevier Science and Academic Press, 2000
  16. Lewanowicz S. Generalized Watson’s summation formula for 3F2(1). Journal of Computational and Applied Mathematics 1997; 86: 375-386
  17. Li NN, Chu W. Terminating balanced 4ϕ3 -series with two integer parameters. Proceedings of the American Mathematical Society 2017; 145 (10): 4371-4383
  18. Li NN, Chu W. Nonterminating 3F2 -series with unit argument. Integral Transforms and Special Functions 2018; 29 (6): 450-469
  19. Prudnikov AP