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Zbl 1131.26005
Srivastava, H.M.
Some bounding inequalities for the Jacobi and related functions. (English)
[J] Banach J. Math. Anal. 1, No. 1, 131-138, electronic only (2007). ISSN 1735-8787/e

The paper describes establishment of bounding inequalities for the Jacobi function as a consequence of reasonably sharp inequalities for the classical Laguerre functions, given in Section 2 of the paper in the form of four lemmas. By virtue of hypergeometric representations of the classical Jacobi function $P^{(\alpha,\beta)}_\upsilon(z)$ $(\upsilon\in C)$ of the first kind and the classical Laguerre function $L^{(\mu)}_\upsilon(z)$ $(\upsilon\in C)$ in terms of ${_1F_1}(\cdot)$, the Eulerian integral is written and then appealing to the corresponding version of Love's inequality, the first bounding inequality is obtained. Further, the lemmas those given in Section 2 are employed to obtain remaining two bounding inequalities.
[P. K. Banerji (Jodhpur)]

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
33C45 Orthogonal polynomials and functions of hypergeometric type
26D15 Inequalities for sums, series and integrals of real functions
33C15 Confluent hypergeometric functions

Keywords: Jacobi functions; Laguerre functions; Bessel functions; Riemann-Liouville fractional derivative operator

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