A Generalized Freud Weight

Full Quadrature Sums for Generalized Polynomials with Freud Weights

Generalized nonnegative polynomials are defined as products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. In this paper we extend quadrature sums involving pth powers of polynomials to those for generalized polynomials.

Generalized Eigenspaces & Generalized Weight Spaces

Freud

A Note on Finite Quadrature Rules with a Kind of Freud Weight Function

We introduce a finite class of weighted quadrature rules with the weight function |x|−2a exp −1/x2 on −∞,∞ as ∫−∞|x|−2a exp −1/x2 f x dx ∑n i 1 wif xi Rn f , where xi are the zeros of polynomials orthogonal with respect to the introduced weight function, wi are the corresponding coefficients, andRn f is the error value. We show that the above formula is valid only for the finite values of n. In...

Sigmund Freud: A New Appraisal

The title of this book is misnamed. More correctly it is an introduction to German psychiatry. Written by the Professor of Psychiatry at the University of Munich, it attempts to present an accurate survey of the history of psychiatry from the 18th century to the present time for an audience which differs widely in interest and sophistication. Whenever an author attempts to write for a group of ...