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A General Turán Expression for the Zeta Function

Published online by Cambridge University Press:  20 November 2018

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In 1948 Gabor Szegő [9] gave four proofs of a remarkable inequality communicated to him by Paul Turán, who later published an original proof [10]. The Turán theorem states that if Pn(x) is the Le gendre polynomial, then

1.1

with equality holding only when |x| = 1.

Since then many similar inequalities have been found for various special functions, particularly for the Legendre and Hermite polynomials. Reference may be had to the recent work of Danese [2] and Chatterjea [1]. Danese gives an extensive bibliography.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1963

References

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