PlanetMath: Gauss' digamma theorem

(more info)

Math for the people, by the people.

Main Menu

sections Encyclopædia
Papers
Books
Expositions

meta Requests (211)
Orphanage
Unclass'd (1)
Unproven (472)
Corrections (36)
Classification

talkback Polls
Forums
Feedback
Bug Reports

downloads Snapshots
PM Book

information News
Docs
Wiki
ChangeLog
TODO List
Legalese
About

Entry average rating: No information on entry rating

Gauss' digamma theorem

(Theorem)

Theorem (Gauss).

$\displaystyle \Psi(x+n)=\frac{1}{x}+\frac{1}{x+1}+\cdots+\frac{1}{x+n-1}+\Psi(x), n=1,2,3,\ldots$

$\displaystyle \Psi\left(\frac{p}{q}\right)=-\gamma-\frac{\pi}{2}\cot{\frac{\pi ... ...{q}+\sum_{n=1}^{q-1} \cos\frac{2\pi n p}{q}\ln\left(2\sin\frac{\pi n}{q}\right)$

where

"Gauss' digamma theorem" is owned by rm50.

(view preamble)

This object's parent.

Attachments:: proof of Gauss' digamma theorem (Proof) by rm50

Log in to rate this entry.
(view current ratings)

Cross-references: Gauss

This is version 3 of Gauss' digamma theorem, born on 2006-11-11, modified 2006-11-12.
Object id is 8542, canonical name is GaussDigammaTheorem.
Accessed 616 times total.

Classification:

AMS MSC:	33B15 (Special functions :: Elementary classical functions :: Gamma, beta and polygamma functions)
	30D30 (Functions of a complex variable :: Entire and meromorphic functions, and related topics :: Meromorphic functions, general theory)

Pending Errata and Addenda

None.[ View all 1 ]

Discussion

forum policy

No messages.

Interact