- 作者: 周章
- 作者服務機構: 銘傳管理學院統計學系
- 中文摘要: 本文中,考慮一由兩個廣義拉各耳函數及一些基本函數之乘積所構成之積分,導出其所滿足之二階差分方程式,並根據Gautschi定理,証明反向遞迴法可用於此積分之計算。文中亦就以反向遞迴法實際計算此積分時,如何確保其可具有所要求之任何數值精確度,提供辦法。
- 英文摘要: A second-order difference equation is derived for an integral involving the product of two generaliz-ed Laguerre polynomials with some elementary functions. Based on a theorem by Gautschi, a proof isgiven which shows that the technique of backward recurrence is applicable for the computation of theintegral. Prescriptions are given for ensuring any desired numerical accuracy when actually evaluating theintegral by backward recurrence.
- 中文關鍵字: backward recurrence; generalized Laguerre polynomials; confluent hypergeometric function; computation of integral
- 英文關鍵字: --