Formula:9859

Digital Library of Mathematical Functions ID 32.2.E13

${\displaystyle{\displaystyle z(1-z)I\left(\int_{\infty}^{w}\frac{\mathrm{d}t}{\sqrt{t(t-1)(t-z)}}\right)=\sqrt{w(w-1)(w-z)}\*\left(\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+(\delta-\tfrac{1}{2})\frac{z(z-1)}{(w-z)^{2}}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle z}}$: real
• ${\displaystyle{\displaystyle\alpha}}$: arbitrary constant
• ${\displaystyle{\displaystyle I}}$:
• ${\displaystyle{\displaystyle\beta}}$: arbitrary constant
• ${\displaystyle{\displaystyle\gamma}}$: arbitrary constant
• ${\displaystyle{\displaystyle\delta}}$: arbitrary constant
 

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