Gaussian quadratures for the integrals ₀^{∞}𝑒𝑥𝑝(-𝑥²)𝑓(𝑥)𝑑𝑥 and ₀^{𝑏}𝑒𝑥𝑝(-𝑥²)𝑓(𝑥)𝑑𝑥

Abstract

Gaussian quadratures are developed for the evaluation of the integrals given in the title. The weights and abscissae for the semi-infinite integral are given for two through fifteen points with fifteen places. For b = 1 b = 1 , the weights and abscissae are given for two through ten points with fifteen places.