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Results tagged with polynomials
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user 169474
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
1
vote
Growth of the "cube of square root" function
For $-1<h<1$,
$$(1+h)^{3/2}+(1-h)^{3/2} = 2 \sum_{n=0}^{+\infty}{3/2 \choose 2n}h^{2n},$$
where
$${3/2 \choose 2n} = \prod_{k=1}^ {2n} \frac{5/2-k}{k}.$$
For $n \ge 1$, since $(-1)^{2n-2}=1$, we get
$ …
- 3,808
7
votes
Square root of prime numbers
My impression is that you have developed $(x_0-\sqrt{S})^{2^n}$ with Newton binomial formula, separated the terms with even index from the terms with odd index to get an expression of the form $A_n-\s …
- 3,808