DLMF:5.12.E2

MaRDI QIDQ2845

• Label: DLMF:5.12.E2

Digital Library of Mathematical Functions ID 5.12.E2

${\displaystyle{\displaystyle\int_{0}^{\pi/2}{\sin^{2a-1}}\theta{\cos^{2b-1}}\theta\mathrm{d}\theta=\tfrac{1}{2}\mathrm{B}\left(a,b\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}$: beta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle a}}$: real or complex variable
• ${\displaystyle{\displaystyle b}}$: real or complex variable
 

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