Orthogonal polynomials

  • Wilhelm Magnus
  • Fritz Oberhettinger
  • Raj Pal Soni
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 52)


A set of functions {φ n (x)}, real or complex valued, defined over an interval (a, b) is said to be linearly independent if
$${a_1}{\phi _1}(x) + {a_2}{\phi _2}(x) + \cdots {a_n}{\phi _n}(x) \equiv 0$$
is true only when a 1 = a 2 = ⋯ = a n = 0.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

  • Wilhelm Magnus
    • 1
  • Fritz Oberhettinger
    • 2
  • Raj Pal Soni
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA
  2. 2.Oregon State UniversityUSA
  3. 3.International Business Machines CorporationUSA

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