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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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8.38 The beta function (Euler's integral of the first kind): B(x, y)

Integral representation

8.380

1. 

B(x,y)=01tx1(1t)y1dt*=201t2x1(1t2)y1dt[Rex<0,Rey<0]

si681_e  FI II 774(1)

2. 

B(x,y)=20π/2sin2x1Φcos2y1ΦdΦ[Rex<0,Rey<0]

si682_e  KU 10

3. 

B(x,y)=20tx1(1+t)x+ydt=20t2x1(1+t2)x+ydt[Rex<0,Rey<0]

si683_e  FI II 775

4. 

B(x,y)=22yx11(1+t)2x1(1t)2y1(1+t2)x+ydt[Rex<0,Rey<0]

  MO 7

5. 

B(x,y)=01tx1+yy1(1+t)x+ydt=1tx1+yy1(1+t)x+ydt[Re

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