Timeline for Determining a Closed Formula for the Positive Zeroes of the $n^{th}$ Derivatives of the Function $x↦x^{-x}$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2018 at 2:32 | comment | added | Nathaniel Weidman | Very true, but is there anyway that an exact answer can be formulated. I know that some derivatives have more than one real root so in my studies I have focused on the larges root for each derivative. It may be that such a formulation doesn't exist; in which a proof would be accepted at an answer showing that it is impossible to find exact solutions. | |
| Jun 7, 2018 at 1:44 | comment | added | Mark L. Stone | Here are the numerical roots for 1st 30 derivatives per Maple fsolve. Rather multi-nodal. 0.3678794412 1. 1.594172705 2.156081546 2.693037878 0.7698317570 0.8922004122 1.076132692 1.297019230 1.551075081 1.836655380 2.149997442 2.484434915 2.832475855 3.188064676 3.547210496 3.907546791 4.267731451 6.550697400 4.984984445 5.341414895 3.785444605 3.679466558 3.837551474 4.023299304 4.227416876 4.446526524 4.679075468 4.924146178 5.180922002 | |
| Jun 7, 2018 at 0:54 | comment | added | Nathaniel Weidman | That is an interesting result, I was thinking only about the positive real roots but looking at the complex roots might give me a better understanding of what is going on between the derivatives. What about the third derivative? | |
| Jun 7, 2018 at 0:43 | comment | added | Mark L. Stone | Here are the roots of the 2nd derivative, per Maple: 1, exp(2*LambertW(-(1/2)*exp(1/2))-1) | |
| Jun 7, 2018 at 0:36 | review | First posts | |||
| Jun 7, 2018 at 2:13 | |||||
| Jun 7, 2018 at 0:36 | history | asked | Nathaniel Weidman | CC BY-SA 4.0 |