Coefficients of a factorial polynomial / polynom
 Factorial polynom Result of the transfer to a usual polynomial

A rather rare calculator for its use in ordinary, mundane life. Factorial polynomials are used to study and calculate finite differences.

Do you get it?

If I had been told this six months ago, I would haven’t understood anything either ... what are the differences, why are they finite ...

This is not studied at schools, at most institutes too.

Finite differences are nevertheless used to solve differential equations.

But about them later, and now I want to introduce the reverse conversion of a factorial polynomial into a regular one. We already know how to do a direct conversion to a factorial polynomial , and in the field of complex numbers too.

It remains to solve the inverse problem.

Theoretical calculations will again be later, when more time appears, and now examples

Turn into a normal form, a given factorial polynomial

$x^{(4)}+(1)$

We hammer in the input field the coefficients 1 0 0 0 1

and get

$x^{4}+(-6)*x^{3}+(11)*x^{2}+(-6)*x^{1}+(1)$

Second example: a factorial polynomial is given by

$-8*x^{(6)}+i*x^{(5)}+(1-i)*x^{(3)}+3*x^{(2)}+i$

determine its normal form

Enter the coefficients -8 i 0 1-i 3 0 i in the input field and get

$(-8)*x^{6}+(120+1i)*x^{5}+(-680-10i)*x^{4}+(1801+34i)*x^{3}+(-2192-47i)*x^{2}+(959+22i)*x^{1}+(0+1i)$

Good calculations !!

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