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Research Articles

Novel summation formulas for Jacobi and Gegenbauer polynomials

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Pages 81-90 | Received 15 Jan 2021, Accepted 09 Mar 2021, Published online: 21 Mar 2021

References

  • Erdélyi A. Higher transcendental functions. Vol. 2 (Bateman project). New York (NY): McGraw-Hill Book Company; 1953.
  • Rainville ED. Special functions. New York (NY): Chelsea Publ. Company; 1960.
  • Brychkov YuA. Handbook of special functions: derivatives, integrals, series and other formulas. Boca Raton (FL): Chapman & Hall/CRC; 2008.
  • Griffiths DJ, Schroeter DF. Introduction to quantum mechanics. 3rd ed. Cambridge: Cambridge University Press; 2018.
  • De R, Dutt R, Sukhatme U. Mapping of shape invariant potentials under point canonical transformations. J Phys A Math Gen. 1992;25(13):L843–L850.
  • Tričković SB, Stanković MS. On the orthogonality of classical orthogonal polynomials. Integral Transforms Spec Funct. 2003;14(3):271–280.
  • Weber HJ. A simple approach to Jacobi polynomials. Integral Transforms Spec Funct. 2007;18(3):217–221.
  • Liu S-J, Lin Sh-D, Chen K-Y, et al. Summation identities involving certain classes of polynomials. Integral Transforms Spec Funct. 2013;24(2):84–97.
  • Conway JT. Indefinite integrals for some orthogonal polynomials obtained using integrating factors. Integral Transforms Spec Funct. DOI:https://doi.org/10.1080/10652469.2020.1786382
  • Conway JT. Indefinite integrals involving Jacobi polynomials from integrating factors. Integral Transforms Spec Funct. DOI:https://doi.org/10.1080/10652469.2020.1844197
  • Šamaj L, Bajnok Z. Introduction to the statistical physics of integrable many-body systems. Cambridge: Cambridge University Press; 2013.
  • Jancovici B. Exact results for the two-dimensional one-component plasma. Phys Rev Lett. 1981;46(6):386–388.
  • Šamaj L, Percus JK. A functional relation among the pair correlations of the two-dimensional one-component plasma. J Stat Phys. 1995;80(3–4):811–824.
  • Šamaj L. Is the two-dimensional one-component plasma exactly solvable?. J Stat Phys. 2004;117(1–2):131–158.
  • Wünsche A. Generating functions for products of special Laguerre 2D and Hermite 2D polynomials. Appl Math. 2015;6(12):2142–2168.
  • Gradshteyn IS, Ryzhik IM. Table of integrals, series and products. 6th ed. New York (NY): Academic Press; 2000.
  • Feldheim E. Contributions à la théorie des polynômes de Jacobi. Mat Fiz Lapok. 1941;48:453–504.
  • Feldheim E. Relations entre les polynômes de Jacobi, Laguerre et Hermite. Acta Math. 1942;75:117–138.
  • Wolfram S. The mathematica book. 5th ed. Champaign (IL): Wolfram Media; 2003.
  • Cohl HS. On a generalization of the generating function for Gegenbauer polynomials. Integral Transform Spec Funct. 2013;24(10):807–816.
  • Maier RS. Algebraic generating functions for gegenbauer polynomials. In: Frontiers in orthogonal polynomials and q-series. London: World Scientific; 2018. Chapter 22. p. 425–444.

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