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- Orthogonal_functions abstract "In mathematics, two functions and are called orthogonal if their inner product is zero for f ≠ g. How the inner product of two functions is defined may vary depending on context. However, a typical definition of an inner product for functions iswith appropriate integration boundaries. Here, the asterisk indicates the complex conjugate of f.For another perspective on this inner product, suppose approximating vectors and are created whose entries are the values of the functions f and g, sampled at equally spaced points. Then this inner product between f and g can be roughly understood as the dot product between approximating vectors and , in the limit as the number of sampling points goes to infinity. Thus, roughly, two functions are orthogonal if their approximating vectors are perpendicular (under this common inner product).[1]Solutions of linear differential equations with boundary conditions can often be written as a weighted sum of orthogonal solution functions (a.k.a. eigenfunctions).Examples of sets of orthogonal functions:Sines and cosinesBessel functionsHermite polynomialsLegendre polynomialsSpherical harmonicsWalsh functionsZernike polynomialsChebyshev polynomials".
- Orthogonal_functions wikiPageExternalLink ?page_id=369.
- Orthogonal_functions wikiPageID "453041".
- Orthogonal_functions wikiPageRevisionID "594682477".
- Orthogonal_functions hasPhotoCollection Orthogonal_functions.
- Orthogonal_functions subject Category:Functional_analysis.
- Orthogonal_functions comment "In mathematics, two functions and are called orthogonal if their inner product is zero for f ≠ g. How the inner product of two functions is defined may vary depending on context. However, a typical definition of an inner product for functions iswith appropriate integration boundaries.".
- Orthogonal_functions label "Funciones ortogonales".
- Orthogonal_functions label "Orthogonal functions".
- Orthogonal_functions label "Ортогональные функции".
- Orthogonal_functions label "直交関数列".
- Orthogonal_functions sameAs Funciones_ortogonales.
- Orthogonal_functions sameAs 直交関数列.
- Orthogonal_functions sameAs m.02bbg_.
- Orthogonal_functions sameAs Q2637908.
- Orthogonal_functions sameAs Q2637908.
- Orthogonal_functions wasDerivedFrom Orthogonal_functions?oldid=594682477.
- Orthogonal_functions isPrimaryTopicOf Orthogonal_functions.