Post Closed as "Needs details or clarity" by Ricardo Andrade, Andrey Rekalo, Daniel Moskovich, Olivier Benoist, Stefan Kohl♦

occurred Nov 28, 2013 at 10:16

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edited Oct 30, 2009 at 5:06

Halfdan

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From an elementary question in differential entropy for decision sequences...

Numerical solutions is: x = 2.293166287408052...

The equality is only well defined (with respect to its origination) in the real domain for x>0. There are obviously an infinite number of solutions in the complex domain.

I have found a continued fraction solution, but have not been able to come up with a closed form variant.

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edited Oct 30, 2009 at 4:35

Halfdan

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Algebraic Closed form solution to x^(x+1)=(x+1)^x

From an elementary question in differential entropy for decision sequences...

Numerical solutions is: x = 2.293166287408052...

The equality is only well defined in the real domain for x>0.

I have found a continued fraction solution, but have not been able to come up with a closed form variant.

Post Reopened by Kim Morrison

occurred Oct 30, 2009 at 4:34

Post Closed as "too localized" by Kim Morrison

occurred Oct 30, 2009 at 4:06

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edited Oct 30, 2009 at 3:53

Halfdan

33
2

From an elementary question in differential entropy for decision sequences...

Numerical solutions is: x = 2.293166287408052...

The equality is only well defined in the real domain for x>0.

Source Link

asked Oct 30, 2009 at 3:29

Halfdan

33
2

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Algebraic Closed form solution to x^(x+1)=(x+1)^x

Algebraic solution to x^(x+1)=(x+1)^x

Closed form solution to x^(x+1)=(x+1)^x