 # Introduction Pairs of Recurrence Relations Recurrences of Smaller Order Conclusion

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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

Subjects

##### Taylor series

Informations

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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 2eRfosriaecnerrucront1I/2nPioctdufomScnseOrdrlaeltionRelaurresRecleAndxanoisoCreulcnerSerieszedFourieGenarilereBontilEiantreeDiarneiLfosnoituloSrof.
I
Introduction
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Some Examples
f(x) =Xanψn(x)
sin(x) = 2X(1)nJ2n(x) n=0 42T2n+x arccos (x=12)πT0(x)n=X0(2n+ 1)π1( ) erf(x) = 2Xx 014nπ(2n+)11n!1F12nn++122n= More generally (ψn(x))nNcan be an orthogonal basis of a Hilbert space.
erentialEquationnoitLfosaeniiDrrSieieerorsfluSorodu1Int3/2 