The Beta function can be expressed in alternative form by substituting

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4.42. The Beta function can be expressed in alternative
form by substituting
1 = sin*e; 1-1= cos²e
(a) Show that
r/2
B(x, y) = 2
sinx-'0 . cos²y-'e de
(b) Now, use the substitution t=cos²0, repeat the
process in (a) and thereby prove
B(x, y) = B(y, x)
Transcribed Image Text:4.42. The Beta function can be expressed in alternative form by substituting 1 = sin*e; 1-1= cos²e (a) Show that r/2 B(x, y) = 2 sinx-'0 . cos²y-'e de (b) Now, use the substitution t=cos²0, repeat the process in (a) and thereby prove B(x, y) = B(y, x)
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