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Interesting Integral
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apov...@gmail.com
Apr 18, 2017, 6:11:16 PM4/18/17
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Per
https://math.stackexchange.com/questions/2230651/a-conjectured-continued-
fraction-for-phi-phi
integrating from 0 to infinity of the function:
e^(-x*(2+(1+sqrt(5))/2))*(cosh(x)+sqrt(5)*sinh(x))^((1+sqrt(5))/2)
is supposed to be:
(phi^phi - 1/phi)/2
where phi =(sqrt(5)+1)/2
Maxima can't find this result symbolically, but numerical integration
gives the expected result.
What about other computer algebra systems?
https://math.stackexchange.com/questions/2230651/a-conjectured-continued-
fraction-for-phi-phi
integrating from 0 to infinity of the function:
e^(-x*(2+(1+sqrt(5))/2))*(cosh(x)+sqrt(5)*sinh(x))^((1+sqrt(5))/2)
is supposed to be:
(phi^phi - 1/phi)/2
where phi =(sqrt(5)+1)/2
Maxima can't find this result symbolically, but numerical integration
gives the expected result.
What about other computer algebra systems?
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