Computation of Incomplete Gamma Functions Γ(a, x)for x≥1

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  • Nakayama Isao
    Department of Decision Sciences and Management Information Systems, Nagoya University of Commerce and Business Administration

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  • x≥1のときの不完全ガンマ関数Γ(a, x)の数値計算
  • x≧1のときの不完全ガンマ関数Γ(a,x)の数値計算
  • x 1 ノ トキ ノ フカンゼン ガンマ カンスウ ガンマ a x ノ スウチ ケイサン

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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.

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