On the Functional Equation f ( λ ) + f ( ω λ ) f ( ω - 1 λ ) = 1 , ( ω 5 = 1 )

Yasutaka Sibuya

Recherche Coopérative sur Programme n°25 (1984)

  • Volume: 34, page 91-103

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Sibuya, Yasutaka. "On the Functional Equation $f(\lambda )+f(\omega \lambda )f(\omega ^{-1}\lambda )=1$, $(\omega ^5=1)$." Recherche Coopérative sur Programme n°25 34 (1984): 91-103. <http://eudml.org/doc/274587>.

@article{Sibuya1984,
author = {Sibuya, Yasutaka},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {91-103},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {On the Functional Equation $f(\lambda )+f(\omega \lambda )f(\omega ^\{-1\}\lambda )=1$, $(\omega ^5=1)$},
url = {http://eudml.org/doc/274587},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Sibuya, Yasutaka
TI - On the Functional Equation $f(\lambda )+f(\omega \lambda )f(\omega ^{-1}\lambda )=1$, $(\omega ^5=1)$
JO - Recherche Coopérative sur Programme n°25
PY - 1984
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 34
SP - 91
EP - 103
LA - eng
UR - http://eudml.org/doc/274587
ER -

References

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  1. 1) I. Bakken, A multiparameter eigenvalue problem in the complex plane, Amer. J. of Math., 99 (1977) 1015-1044 ; Zbl0379.34021MR508244
  2. 2) P. F. Hsieh and Y. Sibuya, On the asymptotic integration of second order linear ordinary differential equations with polynomial coefficients, J. Math. Ana. Appl., 16 (1966) 84-103 ; Zbl0161.05803MR200512
  3. 3) E. R. Kolchln, Differential Algebra and Algebraic Groups, Academic Press, 1973 Zbl0264.12102MR568864
  4. 4) W. Messing and Y. Sibuya, A generalization of Theorem 90 of Hilbert, under preparation ; 
  5. 5) Y. Sibuya and R. Cameron, An entire solution of the functional equation f ( λ ) + f ( ω λ ) f ( ω - 1 λ ) = 1 , ( ω 5 = 1 ) Proc. of Symposium on Ordinary Differential Equations at Univ. of Minnesota, May 29-30, 1972, Lecture Notes in Math., No. 312, 194-202, Springer-Verlag, 1073 ; Zbl0256.30003MR390336
  6. 6) Y. Sibuya, Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient, Math. Studies18, North-Holland, 1975 ; Zbl0322.34006MR486867
  7. 7) A. Voros, The return of the quartic oscillator. The complex WKB method, Ann. Inst. Henri Poincaré, Section A: Physique théorique, 39 (1983) 211-338 ; Zbl0526.34046MR729194
  8. 8) A. Voros, The zeta function of the quartic oscillator, Nuclear Physics B165 (1980) 209-236 ; 
  9. 9) W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, John Wiley, 1965. Zbl0133.35301MR203188

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