Picone's Theorem
Let 
be integrable in 
, let 
be of bounded variation in , let 
denote the least upper boundof 
in , and let 
denote the total variation of 
in . Given the function
then the terms of its Legendre Series
where
is a Legendre Polynomial, satisfy the inequalities
for
(Sansone 1991).See also Jackson's Theorem, Legendre Series
References
Picone, M. Appunti di Analise Superiore. Naples, Italy,, p. 260, 1940. Sansone, G. Orthogonal Functions, rev. English ed. New York: Dover, pp. 203-205, 1991.
- Hermitian Operator
- Hermit Point
- Heronian Tetrahedron
- Heronian Triangle
- Heron's Formula
- Heron Triangle
- Herschel
- Herschfeld's Convergence Theorem
- Hessenberg Matrix
- Hesse's Theorem
- Hessian Covariant
- Hessian Determinant
- Heteroclinic Point
- Heterogeneous Numbers
- Heterological Paradox
- Heteroscedastic
- Heterosquare
- Heuman Lambda Function
- Heun's Differential Equation
- Heuristic
- Hexa
- Hexabolo
- Hexacontagon
- Hexacronic Icositetrahedron
- Hexad