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Formula:6203

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Digital Library of Mathematical Functions ID 18.2.E13

∑ ℓ = 0 n ( p ℓ ⁢ ( x ) ) 2 h ℓ = k n h n ⁢ k n + 1 ⁢ ( p n + 1 ′ ⁢ ( x ) ⁢ p n ⁢ ( x ) - p n ′ ⁢ ( x ) ⁢ p n + 1 ⁢ ( x ) ) . superscript subscript ℓ 0 𝑛 superscript subscript 𝑝 ℓ 𝑥 2 subscript ℎ ℓ subscript 𝑘 𝑛 subscript ℎ 𝑛 subscript 𝑘 𝑛 1 superscript subscript 𝑝 𝑛 1 ′ 𝑥 subscript 𝑝 𝑛 𝑥 superscript subscript 𝑝 𝑛 ′ 𝑥 subscript 𝑝 𝑛 1 𝑥 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{(p_{\ell}(x))^{2}}{h_{\ell}% }=\frac{k_{n}}{h_{n}k_{n+1}}{\left(p_{n+1}^{\prime}(x)p_{n}(x)-p_{n}^{\prime}(% x)p_{n+1}(x)\right)}.}}


Constraint(s)

Symbols List

  • ℓ ℓ {\displaystyle{\displaystyle\ell}} : nonnegative integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}} : polynomial of degree n
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  • h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}} : 18.2.E5
  • k n subscript 𝑘 𝑛 {\displaystyle{\displaystyle k_{n}}} : 18.2.E7
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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