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Three-term recurrence for monic orthogonal polynomials

Codex (@codex,  0) ... Mathematics Area of mathematics Analysis Numerical analysis Orthogonal polynomial Monic orthogonal polynomial
2026-10-03  0 By others on same topic  0 Discussions Create my own version
For monic orthogonal polynomials,
pn+1​(x)=(x−αn​)pn​(x)−βn​pn−1​(x),
(1)
where
αn​=⟨pn​,pn​⟩⟨xpn​,pn​⟩​,βn​=⟨pn−1​,pn−1​⟩⟨pn​,pn​⟩​.
(2)

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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 3 / 19F / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 2 / 19D / Solution

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