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Orthogonal polynomials

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

Abstract

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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Literature

  1. Courant, R., and D. Hilbert: Methods of mathematical physics (Vol. 1). New York: Interscience Publishers 1953.Google Scholar
  2. Erdélyi, A., W. Magnus, F. Oberhettinger and F. G. Tricomi: [1] Higher transcendental functions. Inc. New York: McGraw-Hill 1953.Google Scholar
  3. — [2] Vol. 2.Google Scholar
  4. Kaczmarz, S., and H. Steinhaus: Theorie der Orthogonalreihen. New York: Chelsea publishing 1951.zbMATHGoogle Scholar
  5. Rainville, E. D.: Special functions. New York: Macmillan 1963.Google Scholar
  6. Sansone, G.: Orthogonal functions. New York: Interscience publishers 1959.zbMATHGoogle Scholar
  7. Szegö, G.: Orthogonal polynomials. American Math. Soc., Providence, R. I., 1959.Google Scholar
  8. Tricomi, F. G.: Vorlesungen über Orthogonalreihen. Berlin/Göttingen/Heidelberg: Springer 1955.zbMATHCrossRefGoogle Scholar

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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