Spoiler:

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- Jan 16th 2011, 09:56 PMchiph588@
- Jan 16th 2011, 09:58 PMDrexel28
- Jan 17th 2011, 12:46 PMRandom Variable
- Jan 17th 2011, 12:51 PMchiph588@
- Jan 17th 2011, 04:38 PMRandom Variable
More "fun" with the polygamma function.

EDIT: Show that .

Then use the result to find . - Jan 17th 2011, 08:34 PMDrexel28
- Jan 17th 2011, 09:09 PMRandom Variable
- Jan 17th 2011, 09:13 PMDrexel28
- Jan 17th 2011, 09:28 PMRandom Variable
I'm well aware of that integral. But does ?

And I thought . Nevermind. (Giggle) - Jan 17th 2011, 09:35 PMDrexel28
- Jan 18th 2011, 02:51 PMchiph588@
For , evaluate

Not too difficult, but the result is somewhat surprising if you've never seen it. - Jan 18th 2011, 10:23 PMDrexel28
- Jan 19th 2011, 12:11 AMDrexel28
Try this:

- Jan 19th 2011, 01:23 PMBruno J.
That's just Gauss' hypergeometric series...

This thread has started as "Prove some identities", and has become "Use this transcendental function's properties as proven in Whittaker and Watson". There's nothing wrong with it, but it'd be fun to go back to some relatively simple stuff.

Here's an easy problem I made up : show that, for any positive integer , we have

- Jan 30th 2011, 12:40 PMBruno J.
I didn't mean to kill this thread! Somebody must have solved the problem I gave but forgotten to post their solution... right? ^^