101. The gamma function, which plays an important role in advanced applications, is defined for n > 1 by I(n) = | t"-le+ dt (a) Show that the integral defining r(n) converges for n > 1 (it actually converges for all n > 0). Hint: Show that t"-'e- 1 is an integer. Hint: Use (b) repeatedly. Thus, I'(n) provides a way of defining n-factorial when n is not an integer.

101. The gamma function, which plays an important role in advanced applications, is defined for n > 1 by I(n) = | t"-le+ dt (a) Show that the integral defining r(n) converges for n > 1 (it actually converges for all n > 0). Hint: Show that t"-'e- 1 is an integer. Hint: Use (b) repeatedly. Thus, I'(n) provides a way of defining n-factorial when n is not an integer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 41EQ

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