Math Is Fun Forum

ravz181229

Member

Registered: 2014-03-07

Posts: 4

Evaluation of a product of two gamma functions

Qn. Show that if

then,

.

There are quite a few ways to determine values of Gamma functions, but none of them are getting me any close to the required answer. Also, I have failed to figure out the significance of the range of

given. Any hints and help would be greatly appreciated.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Evaluation of a product of two gamma functions

Hi;

It is easy to get here:

but now proving

I can not do. I am pretty sure that it is true but I do not know that identity or how to get it.

The inequality does not seem to serve any purpose at all.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Evaluation of a product of two gamma functions

There is an identity on Wiki that says that Gamma(z)*Gamma(1-z)=pi/sin(pi*z).

Last edited by anonimnystefy (2014-03-07 23:06:41)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Evaluation of a product of two gamma functions

Hi;

Using anonimnystefy's result, mathematica says...

Substituting z = (1/2) - x).

And that completes the proof. Now if I only knew what went on on the RHS of 2 ) and 3) I would understand his proof too.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Evaluation of a product of two gamma functions

What do you not understand?

Last edited by anonimnystefy (2014-03-08 11:35:58)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Evaluation of a product of two gamma functions

Hi anonimnystefy;

I think I got it now.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ravz181229

Member

Registered: 2014-03-07

Posts: 4

Re: Evaluation of a product of two gamma functions

Thank you anonimnystefy and bobbym... I get it now

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Evaluation of a product of two gamma functions

Hi;

Your welcome and welcome to the forum.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ravz181229

Member

Registered: 2014-03-07

Posts: 4

Re: Evaluation of a product of two gamma functions

Bobbym, to get from step 2 to 3 you use the result  sin(pi/2 - x) = cos(x).

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Evaluation of a product of two gamma functions

Hi;

Thanks, I figured that right after I posted #4. Forgot to edit it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.