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Currently displaying 1 – 5 of 5

Order by Relevance | Title | Year of publication

On deficiencies of small functions for Painlevé transcendents of the fourth kind.

Shimomura, Shun — 2002

Annales Academiae Scientiarum Fennicae. Mathematica

Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation

Shun Shimomura — 2000

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Algebraic independence results for reciprocal sums of Fibonacci numbers

Carsten Elsner; Shun Shimomura; Iekata Shiokawa — 2011

Acta Arithmetica

Algebraic relations for reciprocal sums of Fibonacci numbers

Carsten Elsner; Shun Shimomura; Iekata Shiokawa — 2007

Acta Arithmetica

Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values

Carsten Elsner; Shun Shimomura; Iekata Shiokawa — 2009

Journal de Théorie des Nombres de Bordeaux

We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.

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