@techreport{oai:ipsj.ixsq.nii.ac.jp:00210002,
 author = {平山, 弘 and 小宮, 聖司 and Hiroshi, Hirayama and Seiji, Komiya},
 issue = {4},
 month = {Mar},
 note = {有限項で打ち切った Taylor 級数の四則演算および関数計算は，プログラミング言語を使えば容易に行うことができる．C++ 言語や Fortran 等のオペラレーター・オーバーロード機能を使えば非常に使いやすくなる．通常の数値のように扱うことができる．このプログラムを使うと，これらのプログラミング言語で記述された関数は容易に Taylor 展開できる．ループや条件文を含む関数でも容易に Taylor 展開できることを示す．逆関数は，微分方程式で定義できるので，微分方程式をピカールの逐次近似法 (Picard iteration) を使えば容易に Taylor 展開できる．この方法を使って，ガンマ関数の逆数の数値 Taylor 展開を，100 桁の精度で 100 次まで計算した．従来の展開式は，16 桁の精度で 26 次まであったので大幅に精度および次数を拡張した．これによって，30 桁精度や 60 桁精度以上のガンマ関数も容易に計算することができる．, The arithmetic operations and function calculations of Taylor series truncated by finite terms can be easily defined using programming languages. Using an operator overload function such as C ++ or Fortran makes it very easy to use. It can be treated like a numerical calculation. Using this program, functions written in these programming languages can easily be expanded into Taylor series. It is shown that Taylor expansion can be easily performed even with functions including loops and conditional statements. Since the inverse function can be defined by a differential equation, the differential equation can be easily Taylor-expanded by using Picard iteration. Using this method, the reciprocal Taylor expansion of the gamma function was calculated to the 100th order with 100-digit precision. The conventional expansion formula has 16-digit precision up to 26th order, so the precision and order have been greatly expanded. This makes it possible to easily calculate gamma functions with 30-digit precision or 60-digit precision or higher.},
 title = {数学関数の数値的級数展開法},
 year = {2021}
}