Introduction Pairs of Recurrence Relations Recurrences of Smaller Order Conclusion

Alexandre Benoit Generalized

Description

1 / 21 Introduction Pairs of Recurrence Relations Recurrences of Smaller Order Conclusion Generalized Fourier Series for Solutions of Linear Differential Equations Alexandre Benoit, Joint work with Bruno Salvy INRIA (France) February 15, 2011 Alexandre Benoit Generalized Fourier Series for Solutions of Linear Differential Equations.

• linear differential


• pi t0


• smaller order


• hilbert space


• taylor approximation


• ?1 ?0

Sujets

• Series
• Benoît
• Generalization
• Hilbert space
• Taylor series

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 46
• Langue: English

Extrait

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Generalized Fourier Series for Solutions of Linear Differential Equations

Alexandre Benoit, Joint work with Bruno Salvy

INRIA (France)

February 15, 2011

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Introduction

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Some Examples

f(x) = X a n ψ n (x)

∞ sin(x) = 2 X (−1) n J 2n (x) n=0 ∞ 4 2 T 2n+ x arccos (x= 1 2 ) π T 0 (x)− n= X 0 (2n+ 1)π 1 ( ) erf(x) = 2 X  −x ∞ 0  − 1 4  n √ π(2n+)1 1 n! 1 F 1  2n n + + 1 2 2  n= More generally (ψ n (x)) n∈N can be an orthogonal basis of a Hilbert space.

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