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On the Functional Equation $f (λ) + f (ω λ) f (ω^{- 1} λ) = 1$ , $(ω^{5} = 1)$

Yasutaka Sibuya — 1984

Recherche Coopérative sur Programme n°25

An application of newton iteration procedure to $p$ -adic differential equations

Yasutaka Sibuya

Groupe de travail d'analyse ultramétrique

Essential singular points of solutions of an algebraic differential equation.

Tosihusa Kimura; Yasutaka Sibuya — 1975

Journal für die reine und angewandte Mathematik

On the $p$ -adic continuation of the logarithmic derivative of certain hypergeometric functions

Steven Sperber; Yasutaka Sibuya

Groupe de travail d'analyse ultramétrique

A new proof of multisummability of formal solutions of non linear meromorphic differential equations

Jean-Pierre Ramis; Yasutaka Sibuya — 1994

Annales de l'institut Fourier

We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equation $x \frac{d \vec{y}}{d x} = {\vec{G}}_{0} (x) + [λ (x) + A_{0}] \vec{y} + x^{μ} \vec{G} (x, \vec{y}),$ the idea of our proof is to interpret a formal...

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Currently displaying 1 – 5 of 5

On the Functional Equation $f (λ) + f (ω λ) f (ω^{- 1} λ) = 1$ , $(ω^{5} = 1)$

An application of newton iteration procedure to $p$ -adic differential equations

Essential singular points of solutions of an algebraic differential equation.

On the $p$ -adic continuation of the logarithmic derivative of certain hypergeometric functions

A new proof of multisummability of formal solutions of non linear meromorphic differential equations

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

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

An application of newton iteration procedure to p -adic differential equations

Essential singular points of solutions of an algebraic differential equation.

On the p -adic continuation of the logarithmic derivative of certain hypergeometric functions

A new proof of multisummability of formal solutions of non linear meromorphic differential equations

On the Functional Equation $f (λ) + f (ω λ) f (ω^{- 1} λ) = 1$ , $(ω^{5} = 1)$

An application of newton iteration procedure to $p$ -adic differential equations

On the $p$ -adic continuation of the logarithmic derivative of certain hypergeometric functions