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Find the relation ship between confluent hypergeometric function and laguerre polynomials?

Anonymous

∙ 13y ago

Updated: 10/17/2022

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∙ 13y ago

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Q: Find the relation ship between confluent hypergeometric function and laguerre polynomials?

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What is the easiest way to solve a cubic function?

In some cases, you can take the cube root from both sides. In other cases, factoring can be quite simple (for example, if the cubic polinomial has no constant part). But in general, there is no simple way to solve polynomials of degree 3 and higher, and that's why they are usually not included in high-school algebra textbooks. There is a fairly complicated formula for polynomials of degree 3, similarly for degree 4; for degree 5 and higher, it has been proven that no such formula can exist. In any case, some sort of iterative method is usually used in practice. Conceptually, the simplest such method is probably trial and error (evaluate the polynomial for different values, until you get the value of the polynomial close enough to zero; but this is rather slow and probably doesn't work well for complex solutions. There are more efficient methods; the Wikipedia article states that "Numerical approximations of roots of polynomial equations in one unknown is easily done on a computer by the Jenkins-Traub method, Laguerre's method, Durand-Kerner method or by some other root-finding algorithm." None of these algorithms is probably "easy", but the idea is that, once programmed in a computer, it can find the solution quickly.Also:A cubic equation has the formax3+bx2+cx+d= 0 where a=! 0Look at the examples in the related link.

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