## Banach Journal of Mathematical Analysis

### Some bounding inequalities for the Jacobi and related functions

H. M. Srivastava

#### Abstract

The main object of this paper is to present several bounding inequalities for the classical Jacobi function of the first kind. A number of closely-related inequalities for such other special functions as the classical Laguerre function are also considered.

#### Article information

Source
Banach J. Math. Anal., Volume 1, Number 1 (2007), 131-138.

Dates
First available in Project Euclid: 21 April 2009

https://projecteuclid.org/euclid.bjma/1240321563

Digital Object Identifier
doi:10.15352/bjma/1240321563

Mathematical Reviews number (MathSciNet)
MR2350202

Zentralblatt MATH identifier
1131.26005

#### Citation

Srivastava, H. M. Some bounding inequalities for the Jacobi and related functions. Banach J. Math. Anal. 1 (2007), no. 1, 131--138. doi:10.15352/bjma/1240321563. https://projecteuclid.org/euclid.bjma/1240321563

#### References

• A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Tables of Integral Transforms, Vols. I and II, McGraw-Hill Book Company, New York, Toronto and London, 1954.
• E. Gogovcheva and L. Boyadjiev, Fractional extensions of Jacobi polynomials and Gauss hypergeometric function, Fract. Calc. Appl. Anal. 8 (2005), 431–438.
• A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, Vol. 204, Elsevier (North-Holland) Science Publishers, Amsterdam, 2006.
• I. Krasikov, Uniform bounds for Bessel functions, J. Appl. Anal. 12 (2006), 83–91.
• L. Landau, Monotonicity and bounds on Bessel functions, in Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory (Berkeley, California; June 11–13, 1999) (H. Warchall, Editor), pp. 147–154 (electronic), Electron. J. Differential Equations Conference 4, Southwest Texas State University, San Marcos, Texas, 2000.
• E.R. Love, Inequalities for Laguerre functions, J. Inequal. Appl. 1 (1997), 293–299.
• Y.L. Luke, Inequalities for generalized hypergeometric functions, J. Approx. Theory 5 (1972), 41–65.
• Y.L. Luke, Mathematical Functions and Their Approximations, Academic Press, New York, San Francisco and London, 1975.
• S.P. Mirevski, L. Boyadjiev and R. Scherer, On the Riemann-Liouville fractional calculus, $g$-Jacobi functions and $F$-Gauss functions, Appl. Math. Comput. 187 (2007), 315–325.
• A.Ya. Olenko, Upper bound on $\sqrtxJ_\nu(x)$ and its applications, Integral Transform. Spec. Funct. 17 (2006), 455–467.
• T.K. Pogány and H.M. Srivastava, Some improvements over Love's inequality for the Laguerre function, Integral Transform. Spec. Funct. 18 (2007), 351–358.
• Th.M. Rassias and H.M. Srivastava, Some bounds for orthogonal polynomials and other families of special finctions, in Approximation Theory and Applications (Th. M. Rassias, Editor), pp. 177–193, Hadronic Press, Palm Harbor, Florida, 1998.
• H.M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.