"Christoffel-Darboux formula" meaning in English

{
  "etymology_text": "Named after Elwin Bruno Christoffel and Jean Gaston Darboux.",
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      "glosses": [
        "An identity for a sequence of orthogonal polynomials: ∑ⱼ₌₀ⁿ(f_j(x)f_j(y))/(h_j)=(k_n)/(h_nk_n+1)(f_n(y)f_n+1(x)-f_n+1(y)f_n(x))/(x-y) where fⱼ(x) is the jth term of a set of orthogonal polynomials of squared norm hⱼ and leading coefficient kⱼ."
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      "raw_glosses": [
        "(mathematics) An identity for a sequence of orthogonal polynomials: ∑ⱼ₌₀ⁿ(f_j(x)f_j(y))/(h_j)=(k_n)/(h_nk_n+1)(f_n(y)f_n+1(x)-f_n+1(y)f_n(x))/(x-y) where fⱼ(x) is the jth term of a set of orthogonal polynomials of squared norm hⱼ and leading coefficient kⱼ."
      ],
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  "word": "Christoffel-Darboux formula"
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{
  "etymology_text": "Named after Elwin Bruno Christoffel and Jean Gaston Darboux.",
  "forms": [
    {
      "form": "the Christoffel-Darboux formula",
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    {
      "word": "Christoffel-Darboux theorem"
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        "An identity for a sequence of orthogonal polynomials: ∑ⱼ₌₀ⁿ(f_j(x)f_j(y))/(h_j)=(k_n)/(h_nk_n+1)(f_n(y)f_n+1(x)-f_n+1(y)f_n(x))/(x-y) where fⱼ(x) is the jth term of a set of orthogonal polynomials of squared norm hⱼ and leading coefficient kⱼ."
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        "(mathematics) An identity for a sequence of orthogonal polynomials: ∑ⱼ₌₀ⁿ(f_j(x)f_j(y))/(h_j)=(k_n)/(h_nk_n+1)(f_n(y)f_n+1(x)-f_n+1(y)f_n(x))/(x-y) where fⱼ(x) is the jth term of a set of orthogonal polynomials of squared norm hⱼ and leading coefficient kⱼ."
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  "word": "Christoffel-Darboux formula"
}