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2 results

  • OSCILLATION OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS

  • Part of
  • MARTIN CHUAQUI, PETER DUREN, BRAD OSGOOD, DENNIS STOWE
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 79 / Issue 1 / February 2009
    Published online by Cambridge University Press:
    09 February 2009, pp. 161-169
    Print publication:
    February 2009
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  • In this note we study the zeros of solutions of differential equations of the form u′′+pu=0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are given.

  • On the Monotonic Variation of the Zeros of Ultraspherical Polynomials with the Parameters

  • Renato Spigler
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 4 / 01 December 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 472-477
    Print publication:
    01 December 1984
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  • We show that increases with λ, for 0< λ < 1, being the kth zero of the ultraspherical polynomial and f(λ) a suitable function of λ. As a consequence, some inequalities for and an estimate for can be obtained.