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s question, a is a strictly positive number and I(a) := xa-1 e- ,-T dx. 0. I Evaluate I(1). Use integration by parts to show that, for every a > 0, Iα+ 1) α Ι (α ) . uate I(2), I(3), and deduce a formula for I(n) when n E N+. Show that I(1/2) = 2 du . 0.

s question, a is a strictly positive number and I(a) := xa-1 e- ,-T dx. 0. I Evaluate I(1). Use integration by parts to show that, for every a > 0, Iα+ 1) α Ι (α ) . uate I(2), I(3), and deduce a formula for I(n) when n E N+. Show that I(1/2) = 2 du . 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I(a) := s question, a is a strictly positive number and I(a):= xª-l e- dx . Evaluate I(1). Use integration by parts to show that, for every a > 0, I(a + 1) = a I(a). uate I(2), I(3), and deduce a formula for I(n) when n E N+. Show that I(1/2) = 2 du. 0.
Transcribed Image Text:I(a) := s question, a is a strictly positive number and I(a):= xª-l e- dx . Evaluate I(1). Use integration by parts to show that, for every a > 0, I(a + 1) = a I(a). uate I(2), I(3), and deduce a formula for I(n) when n E N+. Show that I(1/2) = 2 du. 0.
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