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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
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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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)
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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