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Zbl 0694.33002
Askey, Richard A.
Graphs as an aid to understanding special functions. (English)
[A] Asymptotic and computational analysis. Conference in honor of Frank W.J. Olver's 65th birthday, Proc. Int. Symp., Winnipeg/Can. 1989, Lect. Notes Pure Appl. Math. 124, 3-33 (1990).

[For the entire collection see Zbl 0689.00009.] \par Graphs can play an important role in suggesting inequalities for special functions. Some classical examples are given, including Todd's observation about the monotonicity of relative maxima of adjacent Legendre polynomials. A new proof is given of this theorem of Szegö. A similar inequality holds for Legendre functions of the second kind $Q\sb n(x)$. This is suggested by a graph in Jahnke and Emde, and proven in a later paper.
[R.A.Askey]

MSC 2000:: *33C05 Classical hypergeometric functions
33C45 Orthogonal polynomials and functions of hypergeometric type
26D05 Inequalities for trigonometric functions and polynomials

Keywords: Legendre polynomials; inequalities

Citations: Zbl 0689.00009

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