navbar-top.gif
btn_spacer.gifHomeTopicsLatestRandomAboutFAQsParticipateAuthoring Areabtn_spacer.gif

False Logarithm Series

In a paper titled "Consideration of Some Series Which Are Distinguished by Special Properties", published in 1753, Leonhard Euler considers . He proves that for non-negative integers , just like , but shows that this function is different from . This Demonstration compares the plots of and for different values of . Red points correspond to pairs of integers on the line .

The series discovered by Euler is an instance of a -series. In fact where is the -polygamma function. It was the finiteness of that Euler used to demonstrate that is indeed different from .
More information is available in Ed Sandifer's column "How Euler Did It" and in the original paper by Euler.
Free Download: Mathematica Player--Runs all Demonstrations & more


Share & Bookmark This Demonstration


Powered by Wolfram Mathematica
Give us your feedback
Give us your feedback

Source page:




 often  occasionally  never

Note: Please do not include anything you consider confidential or proprietary. We will keep your information private. We will not give it to any third party.
Privacy Policy »

©  2008 The Wolfram Demonstrations Project & Contributors    Wolfram Research    Site Index    Terms of Use    Privacy Policy    RSS    Atom