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Exercise 2 Given that a and n are two non-zero natural numbers and that /(a, n) = x"(1 – x)"dx. a.) Show that /(a, n) = /(n,a) and that /(a + 1,n) =(a,n + 1). b.) Show also that /(a, n) – 1(a,n + 1) = 1(a+ 1,n) c.) Deduce that I(a, n + 1) = n+1 I(a,n) n+a+2 nla! d.) Calculate /(a, 0) and show that /(a, n) = (n+ut1)

Exercise 2 Given that a and n are two non-zero natural numbers and that /(a, n) = x"(1 – x)"dx. a.) Show that /(a, n) = /(n,a) and that /(a + 1,n) =(a,n + 1). b.) Show also that /(a, n) – 1(a,n + 1) = 1(a+ 1,n) c.) Deduce that I(a, n + 1) = n+1 I(a,n) n+a+2 nla! d.) Calculate /(a, 0) and show that /(a, n) = (n+ut1)

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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Exercise 2 Given that a and n are two non-zero natural numbers and that /(a, n) = x" (1 - x)"dx. a.) Show that /(a, n) = 1(n, a) and that I(a + 1,n) =(a,n + 1). %3D n+1 b.) Show also that I(a,n) – 1(a,n+ 1) = I(a + 1,n) %3D c.) Deduce that /(a, n + 1) =; n+1 I(a,n) n+a+2 ila! d.) Calculate I(a, 0) and show that I(a, n) = (n+u+1)!
Transcribed Image Text:Exercise 2 Given that a and n are two non-zero natural numbers and that /(a, n) = x" (1 - x)"dx. a.) Show that /(a, n) = 1(n, a) and that I(a + 1,n) =(a,n + 1). %3D n+1 b.) Show also that I(a,n) – 1(a,n+ 1) = I(a + 1,n) %3D c.) Deduce that /(a, n + 1) =; n+1 I(a,n) n+a+2 ila! d.) Calculate I(a, 0) and show that I(a, n) = (n+u+1)!
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