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

[Ztolk]

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.

[tommy1729]

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 ?

[Ztolk]

What is that?

[tommy1729]

What is that?

http://en.wikipedia.org/wiki/Integration...bstitution

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

[tommy1729]

I was playing around with Maple and I noticed that.

=1.995455958

the substitution y = 1/x proves it.

regards

tommy1729

[Ztolk]

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.