DISCRETE AND PSEUDO ORTHOGONALITY FOR A CLASS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS

Authors

  • MAYA LAHIRI Section of Mathematics, Mahila Mahavidyalaya, Banar邸 Hindu University, Varan函 221 005, Uttar Pradesh, India.
  • BAVANARI SATYANARAYANA Department of Mathematics, Nagarjuna University, Post-Graduate Centre, Ongole 523 001, Andhra Pradesh, India.

DOI:

https://doi.org/10.5556/j.tkjm.28.1997.4311

Keywords:

Discrete orthogonality, pesudo orthogonality, generalized hyper­ geometric functions, Laguerre polynomials, a modified Jacobi polynomials

Abstract

In his Ph. D. thesis [11] Satyanarayana defined and studied the generalized hypergeo­ metric functions $I_n^\alpha(x,w)$ and $H_n^\alpha(x,w).$ In the present paper we consider discrete orthogonality for $I_n^\alpha(x,w)$ and pseudo orthogonality for $H_n^\alpha(x,w)$. We also obtain some interesting applications of the results of our investigation.

References

Charles Jordan, Calculus of Finite Differences, Chelsea Publishing Company, New York, 1960.

M. Lahiri and D. Satyanarayana, "A class of generalized hypergeometric functions defined by using a difference operator," Soochow J. Math., 19(1993), 163-171.

M. Lahiri and D. Satyanarayana, "Extended linear and bilinear generating relations for a class of generalized hypergeometric functions," Indian J. Pure Appl. Math., 24(1993), 705-710.

M. Lahiri and B. Satyanarayana, "Some generating functions for a class of generalized hypergeometric functions," Soochow J. Math., 20(1994), 359-363.

M. Lahiri and B. Satyanarayana, "A new class of contiguous function relations for gen­eralized hypergeometric functions by using a difference operator," Kyungpook Math. J., 34(1994), 193-197.

M. Lahiri and B. Satyanarayana, "Certain bilateral generating relations for generalized hypergeometric functions," Proc. Indian Acad. Sci. Math. Sci., 105(1995) 297-301.

M. Lahiri and B. Satyanarayana, "On a generalized hypergeometric function," Internat. J. Math. and Math. Sci., 9(1994).

L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan, London, 1951.

C. L. Parihar and V. C. Patel, "On modified Jacobi polynomials," J. Indian Acad. Math., 1(1979), 41-46.

E. D. Rainville, Special Functions, Macmillan, New York, 1960.

B. Satyanaryana, Discrete hypergeometric functions defined by a difference operator tech­nique, Ph.D. thesis, Banaras Hindu University, Varanasi, India, 1993.

H. M. Srivastava and P. W. Karlesson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1985.

H. M. Srivastava and H. L. Hanocha, A treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.

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Published

1997-12-01

How to Cite

LAHIRI, M., & SATYANARAYANA, B. (1997). DISCRETE AND PSEUDO ORTHOGONALITY FOR A CLASS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS. Tamkang Journal of Mathematics, 28(4), 325-332. https://doi.org/10.5556/j.tkjm.28.1997.4311

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Papers