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ON ONE TRINOMIAL EQUATION AND ITS SOLUTION

Peter Vassilev
장전수학회 (Jangjeon Mathematical Society)|2010.10|Advanced Studies in Contemporary Mathematics|제20권 제4호|pp. 489-497

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참고문헌

키워드

Maclaurin SeriesTrinomial EquationZerosPower Series
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초록

In the paper the question about the solution of the trinomial equation zn - pz - 1 = 0 is studied. It is shown that for p < 0 this equation has exactly one zero in the open interval (0, 1). That zero is expressed in seven different ways as infinite series. The radius of convergence of these series is found.

Abstract

In the paper the question about the solution of the trinomial equation zn - pz - 1 = 0 is studied. It is shown that for p < 0 this equation has exactly one zero in the open interval (0, 1). That zero is expressed in seven different ways as infinite series. The radius of convergence of these series is found.

참고문헌 (11)

  1. Glasser, M., "Hypergeometric functions and the trinomial equation", J. Comput. Appl. Math., 118(1), pp.169~173 (2000)
  2. Fell, H., "The geometry of zeros of trinomial equations", Rend. Circ. Mat. Palermo., 29(2), pp.303~336 (1980)
  3. Cella, O., "Power series and zeroes of trinomial equations", Aequationes Math., 43(1), pp.94~102 (1992)
  4. Dilcher, K. J., "The zeros of a certain family of trinomials", Glasgow Math. J., 34(1), pp.55~74 (1992)
  5. Eagle, A., "Series for all the Roots of a Trinomial Equation", The American Mathematical Monthly, 46(7), pp.422~425 (1939)
  6. Hurwitz A., "Allgemeine Funktionentheorie und Elliptische Funktionen" (1964), Springer-Verlag
  7. G. Pólya, "Problems and Theorems in Analysis, vol.Ⅰ" (1976), Springer
  8. Vassilev-Missana, M., "On an Analytical Solution of the Equation zn - pz - q = 0 (report)", International Conference on Complex Analysis and Applications (1987)
  9. "Cauchy-Hadamard Theorem"[URL]
  10. "Bolzano's Theorem"[URL]
  11. "Rolle's Theorem"[URL]

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