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Gamma function The gamma function is defined by , for p

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 84AE Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 84AE

Gamma function The gamma function is defined by , for p not equal to zero or a negative integer.a. Use the reduction formula to show that ?(p + 1) = p!(p factorial).________________b. Use the substitution x = u2 and the fact that to show .

Step-by-Step Solution:

SOLUTIONWe know that Step 1(a).we need to use the reduction formula to show that The reduction formula is given by This simply means that Using the same reduction formula we can write Thus on continuing this ,we can write ,where Therefore we have proved that

Step 2 of 2

Chapter 7.7, Problem 84AE is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Gamma function The gamma function is defined by , for p