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Formula:10244

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Digital Library of Mathematical Functions ID 33.9.E2

k ⁢ ( k + 2 ⁢ ℓ + 1 ) 2 ⁢ k + 2 ⁢ ℓ + 1 ⁢ a k - 2 ⁢ η ⁢ a k - 1 + ( k - 2 ) ⁢ ( k + 2 ⁢ ℓ - 1 ) 2 ⁢ k + 2 ⁢ ℓ - 3 ⁢ a k - 2 = 0 , 𝑘 𝑘 2 ℓ 1 2 𝑘 2 ℓ 1 subscript 𝑎 𝑘 2 𝜂 subscript 𝑎 𝑘 1 𝑘 2 𝑘 2 ℓ 1 2 𝑘 2 ℓ 3 subscript 𝑎 𝑘 2 0 {\displaystyle{\displaystyle\frac{k(k+2\ell+1)}{2k+2\ell+1}a_{k}-2\eta a_{k-1}% +\frac{(k-2)(k+2\ell-1)}{2k+2\ell-3}a_{k-2}=0,}}


Constraint(s)

k = 1 , 2 , … 𝑘 1 2 … {\displaystyle{\displaystyle k=1,2,\dots}}

Symbols List

  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • ℓ ℓ {\displaystyle{\displaystyle\ell}} : nonnegative integer
  • η 𝜂 {\displaystyle{\displaystyle\eta}} : real parameter
  • a k subscript 𝑎 𝑘 {\displaystyle{\displaystyle a_{k}}} : coefficients
  •  Edit this on Wikidata

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