+ x8 8! ? note y = cos x is an even function (i e cos(?x) =
function apx=costaylor(xn) Calculates the Maclaurin series approximaton to cos(x) using the first n terms in the expansion apx=0; for i=0:n-1
Two-dimensional Fourier cosine series expansion method for pricing financial options M J Ruijter? C W Oosterlee† October 26 2012 Abstract
7 jan 2011 · sum of cosines the Fourier cosine series For a function f(x) defined on x ? [0?] The resulting cosine-series expansion is plotted in
)dx is called the cosine series expansion of f(x) or f(x) is said to be expanded in a cosine series Similarly let f(x) be an odd function on "p
throughout the same interval in terms of the second set of functions {cos X„ x} finally to substitute the latter series into the expansion of the
This extension is called the odd 2L-periodic extension of f(x) The resulting Fourier series expansion is called a half-range expansion for f(x) because it
Hence cos x is a periodic function of the period 2 ? 5 5 Conditions for a Fourier series expansion coefficients are given by Euler's formula
Transforming Fourier Series Half-range Expansions This yields ?1 + 2 ? ( ? 2 ? 4 ? ? ? k=0 cos((2k + 1)?(x ? 1)/2) (2k + 1)2 ) The cosine
1 (a) Show that the Fourier cosine series expansion for cosax on [0?] is given by cosax = 2asin a? ? [ 1 2a2 ? cosx a2 ? 12 + cos 2x a2 ? 22 ? ···]