Spoiler:

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- January 16th 2011, 08:56 PMchiph588@
- January 16th 2011, 08:58 PMDrexel28
- January 17th 2011, 11:46 AMRandom Variable
- January 17th 2011, 11:51 AMchiph588@
- January 17th 2011, 03:38 PMRandom Variable
More "fun" with the polygamma function.

EDIT: Show that .

Then use the result to find . - January 17th 2011, 07:34 PMDrexel28
- January 17th 2011, 08:09 PMRandom Variable
- January 17th 2011, 08:13 PMDrexel28
- January 17th 2011, 08:28 PMRandom Variable
I'm well aware of that integral. But does ?

And I thought . Nevermind. (Giggle) - January 17th 2011, 08:35 PMDrexel28
- January 18th 2011, 01:51 PMchiph588@
For , evaluate

Not too difficult, but the result is somewhat surprising if you've never seen it. - January 18th 2011, 09:23 PMDrexel28
- January 18th 2011, 11:11 PMDrexel28
Try this:

- January 19th 2011, 12:23 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

- January 30th 2011, 11:40 AMBruno J.
I didn't mean to kill this thread! Somebody must have solved the problem I gave but forgotten to post their solution... right? ^^