Formula:2848

Digital Library of Mathematical Functions ID 5.12.E5

${\displaystyle{\displaystyle\int_{0}^{\pi/2}(\cos t)^{a-1}\cos\left(bt\right)\mathrm{d}t=\frac{\pi}{2^{a}}\frac{1}{a\mathrm{B}\left(\frac{1}{2}(a+b+1),\frac{1}{2}(a-b+1)\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re a>0}}$

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
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle a}}$: real or complex variable
• ${\displaystyle{\displaystyle b}}$: real or complex variable
 

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