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# Evaluate (Hint: Change variables to convert the integrand ISBN: 9780201380279 40

## Solution for problem 8P Chapter B

An Introduction to Thermal Physics | 1st Edition

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Problem 8P

Evaluate (Hint: Change variables to convert the integrand to a Gaussian.) Then use the recursion formula to evaluate Step-by-Step Solution:

To evaluate Step 1:

For the positive values of , the Gamma function = ----(1)

Evaluating for = Step 2:

Substituting = in (1) = ---(2) = 2 We know that = 1, therefore the above equation become = 2 -----(3)

Step 3:

From the Gaussian integral, using the result of Gaussian integral = Splitting the limits of the integral, we get = + = Each part is equal and the value for one part is = -----(4)

Step 4:

Applying the result of (4) in (3)

We get = 2( ) = = 1.7725---(5)

Using Recursion formula

To evaluate Step 1:

For any positive value of , the gamma function becomes = ( -1) ----(6)

Substituting =  = ( -1)  =  -----(7)

Step 2:

We know that =  =   = = 0.8862        ----(8)

To evaluate Step 1:

The previous formula is used only for positive values of . When < 0 the gamma function becomes = -----(9) = Step 2 of 2

##### ISBN: 9780201380279

This full solution covers the following key subjects: evaluate, hint, change, formula, gaussian. This expansive textbook survival guide covers 10 chapters, and 454 solutions. The full step-by-step solution to problem: 8P from chapter: B was answered by , our top Physics solution expert on 07/05/17, 04:29AM. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. Since the solution to 8P from B chapter was answered, more than 252 students have viewed the full step-by-step answer. The answer to “Evaluate (Hint: Change variables to convert the integrand to a Gaussian.) Then use the recursion formula to evaluate” is broken down into a number of easy to follow steps, and 18 words. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1.

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