NEW!連分数の性質

\[ \left[\left(a_{0},b_{0}\right);\left(a_{1},b_{1}\right),\cdots,a_{n}+c\right]=\left[\left(a_{0},b_{0}\right);\left(a_{1},b_{1}\right),\cdots,\left(a_{n},b_{n}\right),\frac{b_{n}}{c}\right] \]

NEW!連分数の定義

\[ \left[a_{0};a_{1},a_{2},a_{3},\cdots\right]:=a_{0}+\frac{1}{a_{1}+\frac{1}{a_{2}+\frac{1}{a_{3}+\cdots}}} \]

一般化超幾何関数の微分と積分

\[ \frac{d}{dx}F\left(\boldsymbol{a};\boldsymbol{b};x\right)=\frac{\prod_{i=1}^{\dim\boldsymbol{a}}a_{i}}{\prod_{j=1}^{\dim\boldsymbol{b}}b_{j}}F\left(\boldsymbol{a}+\boldsymbol{1};\boldsymbol{b}+\boldsymbol{1};x\right) \]