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

Updated: 10/17/2022
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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.

Related questions

How do you pronounce Laguerre as in Laguerre polynomials in French?

lah GERRE, with a hard G. I knew a double major in math & French would come in handy someday...

What has the author M Rahman written?

M. Rahman has written: 'The hydrodynamics of waves and tides, with applications' -- subject(s): Water waves, Hydrodynamics 'Construction of a family of positive kernels from Jacobi polynomials' -- subject(s): Jacobi polynomials, Kernel functions, Laguerre polynomials

What has the author Brian Thomas Smith written?

Brian Thomas Smith has written: 'A zero finding algorithm using Laguerre's method' -- subject(s): Algorithms, Polynomials

When was Edmond Laguerre born?

Edmond Laguerre was born in 1834.

When did Edmond Laguerre die?

Edmond Laguerre died in 1886.

When did Louis Laguerre die?

Louis Laguerre died in 1721.

When was Louis Laguerre born?

Louis Laguerre was born in 1663.

What has the author Danielle LaGuerre written?

Danielle LaGuerre has written: 'Black ties'

What is Enrique Laguerre's birthday?

Enrique Laguerre was born on May 6, 1906.

When was Enrique Laguerre born?

Enrique Laguerre was born on May 6, 1906.

When did André Laguerre die?

André Laguerre died on 1979-01-18.

When was André Laguerre born?

André Laguerre was born on 1915-06-07.

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