A Generalized Taylor's Formula for Functions of Several Variables and Certain of its Applications

2021 ◽  
Author(s):  
J A Riestra
Keyword(s):  
Taylor’S Formula ◽  
Several Variables ◽  
Generalized Taylor’S Formula ◽  
Taylor's Formula

ON THE FRACTIONAL MEAN-VALUE THEOREM

2012 ◽  
Vol 22 (05) ◽  
pp. 1250104 ◽  
Author(s):  
PENG GUO ◽  
CHANGPIN LI ◽  
GUANRONG CHEN
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Taylor’S Formula ◽  
New Formulation ◽  
Generalized Taylor’S Formula ◽  
Taylor's Formula

In this paper, we derive a fractional mean-value theorem both in the sense of Riemann–Liouville and in the sense of Caputo. This new formulation is more general than the generalized Taylor's formula of Kolwankar and the fractional mean-value theorem in the sense of Riemann–Liouville developed by Trujillo.

scholarly journals Generalized Vandermonde determinants for reversing Taylor's formula and application to hypoellipticity

2007 ◽  
Vol 38 (2) ◽  
pp. 183-189
Author(s):  
Giuseppe De Donno
Keyword(s):  
Differential Operators ◽  
Partial Differential ◽  
Taylor’S Formula ◽  
Several Variables ◽  
Partial Differential Operators ◽  
Constant Coefficients ◽  
Linear Partial Differential Operators ◽  
Necessary And Sufficient ◽  
Complex Coefficients ◽  
Taylor's Formula

The problem of the hypoellipticity of the linear partial differential operators with constant coefficients was completely solved by H"{o}r-man-der in [5]. He listed many equivalent algebraic conditions on the polynomial symbol of the operator, each necessary and sufficient for hypoellipticity. In this paper we employ two Mitchell's Theorems (1881) regarding a type of Generalized Vandermonde Determinants, for inverting Taylor's formula of polynomials in several variables with complex coefficients. We obtain then a more direct and easy proof of an equivalence for the mentioned H"{o}r-man-der's hypoellipticity conditions.

Generalized Taylor’s formula

2007 ◽  
Vol 186 (1) ◽  
pp. 286-293 ◽  
Author(s):  
Zaid M. Odibat ◽  
Nabil T. Shawagfeh
Keyword(s):  
Taylor’S Formula ◽  
Generalized Taylor’S Formula ◽  
Taylor's Formula
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