Timeline for Transcendental formulas for roots of polynomials
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Jan 25 at 20:05 | comment | added | Тyma Gaidash | It may be that the simpler “Prabhakar function” solves the equation | |
| Apr 13, 2022 at 17:47 | comment | added | IV_ | My answers in the following threads show that there are no solutions in terms of elementary functions / in the elementary numbers. math.stackexchange.com/questions/727534/… math.stackexchange.com/questions/1828551/… math.stackexchange.com/questions/1555743/… math.stackexchange.com/questions/291909/… | |
| Oct 16, 2021 at 6:32 | comment | added | Wlod AA | Charles Hermite and his solution of the quintic equation. | |
| Oct 16, 2021 at 5:35 | answer | added | Jorge Zuniga | timeline score: 5 | |
| Oct 15, 2021 at 15:39 | comment | added | Ira Gessel | For solving the general quintic, see also math.stackexchange.com/questions/540964/… and en.wikipedia.org/wiki/Quintic_function. | |
| Oct 15, 2021 at 13:34 | comment | added | François Brunault | There is Felix Klein's icosahedral solution of the quintic. It can be solved using modular and theta functions for example. See arxiv.org/abs/1308.0955 and arxiv.org/abs/1911.02358 | |
| Oct 15, 2021 at 13:19 | answer | added | Alexandre Eremenko | timeline score: 8 | |
| Oct 15, 2021 at 10:43 | comment | added | Daniele Tampieri | This Q&A is relevant. | |
| Oct 15, 2021 at 7:32 | comment | added | Dave L Renfro | See method of finding roots of polynominal equations with arithmetic operations and roots and other functions AND Are elementary and generalized hypergeometric functions sufficient to express all algebraic numbers? AND Can Fuchsian functions solve the general equation of degree n? | |
| Oct 15, 2021 at 7:20 | comment | added | YCor | An inverse function for a polynomial (e.g., $P$ such that $P(z)^5+P(z)+1=z$) is not something that would qualify as "transcendental", almost by definition. | |
| S Oct 15, 2021 at 7:15 | history | edited | Glorfindel |
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| Oct 15, 2021 at 6:35 | comment | added | Pietro Majer | There is a not too complicated formal power series solution for any polynomial $P(x)$ (that also works for “pseudo-polynomials”, i.e. with non integer exponents) . The series solution is convergent provided the constant term $P(0)$ is relatively not too large (thus it is a perturbation result) mathoverflow.net/questions/249060/… | |
| Oct 15, 2021 at 4:45 | review | Close votes | |||
| Oct 18, 2021 at 22:28 | |||||
| Oct 15, 2021 at 0:59 | review | Suggested edits | |||
| S Oct 15, 2021 at 7:15 | |||||
| Oct 15, 2021 at 0:58 | history | edited | Gbj | CC BY-SA 4.0 |
added 120 characters in body
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| Oct 15, 2021 at 0:57 | comment | added | J. W. Tanner | Cf. this | |
| S Oct 15, 2021 at 0:54 | review | First questions | |||
| Oct 15, 2021 at 4:26 | |||||
| S Oct 15, 2021 at 0:54 | history | asked | Gbj | CC BY-SA 4.0 |