Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » Math Topics » discretemath

Topic: Proof of Irrationality
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  

Posts: 3
Registered: 12/6/04
Proof of Irrationality
Posted: Aug 13, 2010 9:31 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I'd certainly appreciate some help with this question. Thanks in advance, Peter

Let L(x) be the power series

L(x) = sum_{i = 1}^{00} x^{i !} = x + x^2 + x^6 + x^24 + . . . . ,

and let r be some rational such that 0 < r <= ½.

I think that, for all r in the given half-open interval, L(r) is irrational.
Can this be proved ?
Or maybe I are wrong and there is/are just some value(s) of r for which L(r) is irrational.

P.S. Does the series L(x) have a name at all ? I think it is what is known as a Lacunary function (i.e., it has a so called ?natural boundary?)

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.