Nahid R.

asked • 12/22/15

Immediate help

Hi everyone. I have a complex statemant with Gamma functions. I wil be so happy if someone can help me. I have uploaded its formula image in this address:
 
http://s6.picofile.com/file/8229316200/55666666.jpg
 
this formula must reach to (L+3/2)^(-1/2)
 
I don't know how to simplify the gamma functions for achiving above result. Do you have any idea?
 
Thanks a lot
 
 

2 Answers By Expert Tutors

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Jim S. answered • 12/22/15

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Hi Nahid,
             Don't know if this will help you but Γ(n)=(n-1)! !=  factorial n is an integer
If any of the arguments are integers you can replace the gamma functions with the factorial relationship
 
Hope this helps
 
Jim
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Nahid R.

Dear Jim:
thanks for your answer, yes I can covert the gamma functions to factorial, but this don't simplify the statement. I need something which convert power 2 of the gamma function to something else, what I can factor and exit from bracket and finally be removed by denominator. I require the solution very much. I hope someone can help me
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12/22/15

Jim S.

 After you convert the  gramma functions to factorials try using Sterling's approximation for the factorials  then you can square the approximation  maybe ??
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12/22/15

Nahid R.

It seems that such operation can't simplify the statement. can you write exactly what you mean? 
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12/22/15

Eugene E. answered • 12/22/15

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The α's do not cancel in the expression, so the result cannot be (l + 3/2)-1/2. In fact, when α = 1 and l = 0, the expression under the square root is negative, so the resulting answer is not a real number.
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Nahid R.

Thanks Eugene. why α=1 and l=0? I want to solve it parametric. In fact the statement is a part of a article that have been published in Journal of Mathematical Physics a few weeks ago, therefore the given result cannot be false. I look for a trick for canceling gamma function
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12/22/15

Eugene E.

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Certainly, there must be conditions stated in the journal which would imply that the expression you've presented equals (l + 3/2)-1/2. You have not stated the precise conditions, so as presented the result is false, as I've indicated with a counterexample.
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12/22/15

Nahid R.

It has not been mentioned any condition in the article but only point which be stated is this result in the large value of L approches to 0
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12/22/15

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