Explanation Given information: The given Gamma function which is defines as Γ ( n ) = ∫ 0 ∞ t n − 1 e − t d t To prove that Γ ( n ) converges for n ≥ 1 , it is evident to prove that t n − 1 e − t < t − 2 for sufficiently large. Because we know that ∫ 0 ∞ t − 2 d t converges To determine (b) To prove: that Γ ( n + 1 ) = n Γ ( n ) using integration by parts. To determine (c) To prove: that Γ ( n + 1 ) = n if n ≥ 1 is an integer.

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Question

Chapter 7.7, Problem 101E

To determine

(a)

To prove that the integral defining Γ(n) converges for n≥1.

To determine

(b)

To prove:that Γ(n+1)=nΓ(n) using integration by parts.

To determine

(c)

To prove:that Γ(n+1)=n if n≥1 is an integer.

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Chapter 7.7, Problem 100E

Chapter 7.7, Problem 102E

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Chapter 7 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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(a) To prove that the integral defining Γ ( n ) converges for n ≥ 1 .

Solution Summary: The author explains how the integral defining Gamma (n) converges for nge 1.

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(a)

To prove that the integral defining Γ(n) converges for n≥1.

(b)

To prove:that Γ(n+1)=nΓ(n) using integration by parts.

(c)

To prove:that Γ(n+1)=n if n≥1 is an integer.

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Chapter 7 Solutions

(a) To prove that the integral defining Γ ( n ) converges for n ≥ 1 .

Solution Summary: The author explains how the integral defining Gamma (n) converges for nge 1.

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(a) To prove that the integral defining Γ(n) converges for n≥1.

(b) To prove:that Γ(n+1)=nΓ(n) using integration by parts.

(c) To prove:that Γ(n+1)=n if n≥1 is an integer.

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Chapter 7 Solutions

(a)

To prove that the integral defining Γ(n) converges for n≥1.

(b)

To prove:that Γ(n+1)=nΓ(n) using integration by parts.

(c)

To prove:that Γ(n+1)=n if n≥1 is an integer.