Calculate the value of the gamma function for n=10.5 & n=11.5. Then Compare the values to the factorial integral values for n=10,11 & 12. Show how to get l(10.5)= 11899423.08396 And I(11.5)= 136843365.4655 not by numerical integration.
Calculate the value of the gamma function for n=10.5 & n=11.5. Then Compare the values to the factorial integral values for n=10,11 & 12. Show how to get l(10.5)= 11899423.08396 And I(11.5)= 136843365.4655 not by numerical integration.
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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Hi please show all the steps. Thank you
![Calculate the value of the gamma function for n=10.5 & n=11.5. Then
Compare the values to the factorial integral values
for n=10,11 & 12.
Show how to get I(10.5)= 11899423.08396
And 1(11.5)= 136843365.4655 not by numerical integration.
In =
x"e¬* dx
Now using numerical integration we transform it into a sum to get,
I(10.5) 11899423.08396
I(11.5) & 136843365.46556
Now the values for the integers are,
I(10)
= 3628800 ; I(11) = 39916800 ;I(12)
= 479001600
It is seen that,
I(10) < I(10.5) <I(11) < I(11.5) < I(12)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4eea6def-32b0-498a-b503-194af21091f4%2F5fc81e2c-9b58-40b9-8a70-d36d1e577c5f%2Fntenzw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Calculate the value of the gamma function for n=10.5 & n=11.5. Then
Compare the values to the factorial integral values
for n=10,11 & 12.
Show how to get I(10.5)= 11899423.08396
And 1(11.5)= 136843365.4655 not by numerical integration.
In =
x"e¬* dx
Now using numerical integration we transform it into a sum to get,
I(10.5) 11899423.08396
I(11.5) & 136843365.46556
Now the values for the integers are,
I(10)
= 3628800 ; I(11) = 39916800 ;I(12)
= 479001600
It is seen that,
I(10) < I(10.5) <I(11) < I(11.5) < I(12)
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