x≥1のときの不完全ガンマ関数Γ(a, x)の数値計算
2000 年 10 巻 1 号 p. 1-20
詳細
2000 年 10 巻 1 号 p. 1-20
An efficient method for calculating incomplete gamma functions Γ(a, x)for x≥1 is discussed. It is shown that modifying the continued fraction for Γ(a, x)by using appropriate modifying factors yields convergence acceleration with a remarkable reduction of the number of terms required for a given accuracy. In addition sequences of upper and lower bounds for Γ(a, x)are also derived and hence in a wide region of parameters the new method introduced here is proved to be useful at a higher level of accuracy as well as at a lower level.
