In mathematics, the Hermite transform is an
integral transform
In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily charac ...
named after the mathematician
Charles Hermite
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
Hermite p ...
that uses
Hermite polynomials
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.
The polynomials arise in:
* signal processing as Hermitian wavelets for wavelet transform analysis
* probability, such as the Edgeworth series, as well a ...
as kernels of the transform.
The Hermite transform
of a function
is
The inverse Hermite transform
is given by
Some Hermite transform pairs
References
Sources
*{{citation , last1=Erdélyi , first1=Arthur , author-link1=Arthur Erdélyi , last2=Magnus , first2=Wilhelm , author-link2=Wilhelm Magnus , last3=Oberhettinger , first3=Fritz , author-link3=:de:Fritz Oberhettinger , last4=Tricomi , first4=Francesco G. , author-link4=Francesco Tricomi , title=Higher transcendental functions , volume=II , publisher=McGraw-Hill , year=1955 , url=http://apps.nrbook.com/bateman/Vol2.pdf , isbn=978-0-07-019546-2 , access-date=2023-11-09 , archive-date=2011-07-14 , archive-url=https://web.archive.org/web/20110714210423/http://apps.nrbook.com/bateman/Vol2.pdf , url-status=dead
Integral transforms
Mathematical physics