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Self-root function and reciprocal self-power function have same integrals - Printable Version

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Self-root function and reciprocal self-power function have same integrals - Ztolk - 04/03/2010

I was playing around with Maple and I noticed that.

=1.995455958

I then added some parameters and came up with the following:



For positive a and b, and c>2.

I do not know why this is, but I find it very interesting. The self-root function is the inverse of an infinite order tetration.


RE: Self-root function and reciprocal self-power function have same integrals - tommy1729 - 04/07/2010

(04/03/2010, 04:25 AM)Ztolk Wrote: I was playing around with Maple and I noticed that.

=1.995455958

I then added some parameters and came up with the following:



For positive a and b, and c>2.

I do not know why this is, but I find it very interesting. The self-root function is the inverse of an infinite order tetration.

have you tried substitution ?

a moebius substitution ?


RE: Self-root function and reciprocal self-power function have same integrals - Ztolk - 04/07/2010

What is that?


RE: Self-root function and reciprocal self-power function have same integrals - tommy1729 - 04/07/2010

(04/07/2010, 04:04 PM)Ztolk Wrote: What is that?

http://en.wikipedia.org/wiki/Integration_by_substitution

http://en.wikipedia.org/wiki/M%C3%B6bius_transformation

combining the above two and leaving out the restriction ad -bc = 0 if needed.

regards

tommy1729


RE: Self-root function and reciprocal self-power function have same integrals - tommy1729 - 04/10/2010

(04/03/2010, 04:25 AM)Ztolk Wrote: I was playing around with Maple and I noticed that.

=1.995455958

the substitution y = 1/x proves it.

regards

tommy1729


RE: Self-root function and reciprocal self-power function have same integrals - Ztolk - 04/11/2010

So it does. Neat. Thanks.

I should try this with the full three parameter version.

edit: 1/x substitution checks out for the full thing.