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Fungrim entry: 59e5df

Pn(x)(n1)n(n+1)(n+2)8\left|P''_{n}(x)\right| \le \frac{\left(n - 1\right) n \left(n + 1\right) \left(n + 2\right)}{8}
Assumptions:nZ0and1x1n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, -1 \le x \le 1
TeX:
\left|P''_{n}(x)\right| \le \frac{\left(n - 1\right) n \left(n + 1\right) \left(n + 2\right)}{8}

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, -1 \le x \le 1
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
LegendrePolynomialPn ⁣(z)P_{n}\!\left(z\right) Legendre polynomial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("59e5df"),
    Formula(LessEqual(Abs(Derivative(LegendrePolynomial(n, x), Tuple(x, x, 2))), Div(Mul(Mul(Mul(Sub(n, 1), n), Add(n, 1)), Add(n, 2)), 8))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), LessEqual(-1, x, 1))))

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2019-08-17 11:32:46.829430 UTC