Search results with tag "Orthogonal functions"
11.1 ORTHOGONAL FUNCTIONS - Pennsylvania State …
www.personal.psu.eduFor example, the functions f 1(x) x2 and f 2(x) x3 are orthogonal on the interval [ 1, 1], since Unlike in vector analysis, in which the word orthogonal is a synonym for perpendic- ular, in this present context the term orthogonal and condition (1) have no geometric significance. ORTHOGONAL SETSWe are primarily interested in infinite sets of orthogonal
Chapter 10. Fourier Transforms and the Dirac Delta Function
www.physics.sfsu.eduas the Fourier series is an expansion in terms of a series of orthogonal functions. Here is the picture. Basis states The functions e i t 2 1 Ö( ) . (10-21) constitute a complete orthonormal basis for the space of ''smooth'' functions on the interval t . We are not going to prove completeness; as with the Fourier series, the fact that the
1 Solutions in cylindrical coordinates: Bessel functions
www.physics.sfsu.eduis Bessel’s equation. The solutions are orthogonal functions. Since f (0) = 0, we do not need to specify any boundary condition at ρ=0if our range is 0 ≤ρ≤a, as is frequently the case. (We do specify that R remain finite.) We do need a boundary condition at ρ= a. It is simpler and more elegant to solve Bessel’s equation if we change ...
Orthogonal Functions: The Legendre, Laguerre, and Hermite ...
www.math.lsu.eduSturm-Liouville Conclusion Orthogonal Functions: The Legendre, Laguerre, and Hermite Polynomials Thomas Coverson1 Savarnik Dixit3 Alysha Harbour2 Tyler Otto3 1Department of Mathematics Morehouse College 2Department of Mathematics University of Texas at …
ORTHOGONAL FUNCTIONS: THE LEGENDRE, - LSUMath
www.math.lsu.eduTHOMAS2 COVERSON, SAVARNIK DIXIT, ALYSHA HARBOUR, AND TYLER OTTO 2. The Sturm-Liouville Theory A Sturm-Liouville equation is a homogeneous second order di eren-
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Orthogonal functions, Perpendic- ular, Chapter 10. Fourier Transforms and the Dirac Delta, Fourier series, Series, Functions, Bessel functions, Bessel, Orthogonal Functions: The Legendre, Laguerre, Sturm, Orthogonal Functions: The Legendre, Laguerre, and Hermite Polynomials, ORTHOGONAL FUNCTIONS: THE LEGENDRE