Certain generalizations of Jacobi polynomial and their properties
https://doi.org/10.26907/0021-3446-2024-12-20-37
Abstract
Jacobi polynomial $P_{n}^{\left( \alpha ,\beta \right)}(x)$ is a well-known orthogonal polynomial. In the present work, several new properties of generalized Jacobi polynomial $P_{n,\tau}^{\left( \alpha ,\gamma,\beta \right)}(x)$ (Waghela D., Rao S.B. A Note on Sequence of Functions associated with the Generalized Jacobi polynomial, Researches Math. 31 (2), 1-18 (2023)) and its special case $P_{n}^{\left( \alpha ,\gamma,\beta \right)}(x)$ have been studied, which along with different representations of the said generalization includes crucial orthogonality property, generating function, results involving integral representation, differentiation of generalized Jacobi polynomial; also many well-known transformations of this generalized polynomial have been obtained.
About the Authors
D. Waghela
The Maharaja Sayajirao University of Baroda
India
India
Divya Waghela
Vadodara, Gujarat, 390001
S. B. Rao
The Maharaja Sayajirao University of Baroda
India
India
Snehal B. Rao
Vadodara, Gujarat, 390001
References
1. Rainville E.D. Special Functions (The MacMillan Company, New York, 1960).
2. Szegö G. Orthogonal Polynomials, American Mathematical society (Providence, Rhode Island, 1939).
3. Virchenko N., Kalla S.L., Al-Zamel A. Some Results on a Generalized Hypergeometric Function, Integral Transforms and Special Functions 12 (1), 89–100 (2001).
4. Waghela D., Rao S.B. A Note on Sequence of Functions associated with the Generalized Jacobi polynomial, Researches Math. 31 (2), 1–18 (2023).
5. Rao S.B., Prajapati J.C., Shukla A.K. Wright type hypergeometric functions and its properties, Adv. Pure Math. 3 (3), 335–342 (2013).
6. Rao S.B., Shukla A.K. Note on Generalized Hypergeometric Function, Integral Transforms and Special Functions 24 (11), 896–904 (2013).
7. Rao S.B., Patel A.D., Prajapati J.C., Shukla A.K. On Sequence of Functions Containing Generalized Hypergeometric Function, Math. Sci. Research J. 17 (4), 98–110 (2013).
8. Rao S.B. Explicit Representation and Some Integral Transforms of Sequence of Functions Associated with the Wright type Generalized Hypergeometric Function, Global J. Pure and Appl. Math. 13 (9), 6703–6712 (2017).
9. Rao S.B., Patel A.D., Prajapati J.C., Shukla A.K. Some properties of generalized hypergeometric function, Commun. Korean Math. Soc. 28 (2), 303–317 (2013).
10. Rao S.B., Prajapati J.C., Patel A.D., Shukla A.K. Some properties of Wright-type generalized hypergeometric function via fractional calculus, Adv. Diff. Equat. 2014 (119) (2014).
11. Rao S.B. Some Studies on Wright Type Generalized Hypergeometric Function, Ph.D thesis submitted to the Sardar Vallabhbhai National Institute of Technology (SVNIT), Surat, India, 2014.
12. Srivastava H.M., Manocha H.L. A Treatise on Generating Functions (Ellis Horwood, Chichester; John Wiley and Sons, New York, 1984).
13. Sneddon I.N. The Use of Integral Transforms (Tata McGraw-Hill Publ., New Delhi, 1979).
14. Whittaker E.T., Watson G.N. A Course in Modern Analysis, 4th ed. (Cambridge Univ. Press, 1996).
Review
For citations:
Waghela D., Rao S.B. Certain generalizations of Jacobi polynomial and their properties. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(12):20-37. (In Russ.) https://doi.org/10.26907/0021-3446-2024-12-20-37
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