カテゴリー: 超幾何関数

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

\[ \left(1+x\right)^{a}=F\left(-a;;-x\right) \]

\[ x\left(1-x\right)y''\left(x\right)+\left(c-\left(a+b+1\right)x\right)y'\left(x\right)-aby\left(x\right)=0 \]

\[ xy''\left(x\right)+\left(b-x\right)y'\left(x\right)-ay\left(x\right)=0 \]

\[ ak+b=b\frac{Q\left(\frac{b}{a}+1,k\right)}{Q\left(\frac{b}{a},k\right)} \]