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2. Show that: 3(m, n) = 3(n, m) 3(m, n) = √ zm-1 (1+z)m+n 8(n,₁ n) = 2√¹²²(t-1²)n-1 dt dz

2. Show that: 3(m, n) = 3(n, m) 3(m, n) = √ zm-1 (1+z)m+n 8(n,₁ n) = 2√¹²²(t-1²)n-1 dt dz

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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2. Show that: B(m, n) = B(n, m) 3(m, n) = √ zm-1 (1+z)m+n 1/2 3(n,n) = 2 • √ (t - t²)n-1 dt 3. Using gamma function, show that dz ∞ 1.80 e-x² (4x² - 12x² + 3) dx = 0 3(x+1, y) = = 4. Prove that the beta function obeys the following identity: X -B(x, y) x+y= 2592
Transcribed Image Text:2. Show that: B(m, n) = B(n, m) 3(m, n) = √ zm-1 (1+z)m+n 1/2 3(n,n) = 2 • √ (t - t²)n-1 dt 3. Using gamma function, show that dz ∞ 1.80 e-x² (4x² - 12x² + 3) dx = 0 3(x+1, y) = = 4. Prove that the beta function obeys the following identity: X -B(x, y) x+y= 2592
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