Function Approximations Package (Function Approximations Package Tutorial)

This loads the package. Economized rational approximations. A Pad é approximation is very accurate near the center of expansion, but the error increases rapidly as you get ...

Eigensystem (Built-in Mathematica Symbol)

Eigensystem[m] gives a list {values, vectors} of the eigenvalues and eigenvectors of the square matrix m. Eigensystem[{m, a}] gives the generalized eigenvalues and ...

FixedStep Method for NDSolve (Mathematica Tutorial)

It is often useful to carry out a numerical integration using fixed step sizes. For example, certain methods such as "DoubleStep" and "Extrapolation" carry out a sequence of ...

ExpandAll (Built-in Mathematica Symbol)

ExpandAll[expr] expands out all products and integer powers in any part of expr. ExpandAll[expr, patt] avoids expanding parts of expr that do not contain terms matching the ...

ExistsRealQ (Experimental Package Symbol)

ExistsRealQ[ineqs, {x_1, x_2, ...}] tests whether there exist real values of the x_i for which the inequalities and equations ineqs are satisfied.

ForAllRealQ (Experimental Package Symbol)

ForAllRealQ[ineqs, {x_1, x_2, ...}] tests whether for all real values of the x_i the inequalities and equations ineqs are satisfied.

ImpliesRealQ (Experimental Package Symbol)

ImpliesRealQ[ineqs_1, ineqs_2] tests whether the inequalities and equations ineqs_1 imply the ineqs_2 for all real values of all variables.

Function Approximations Package ... (Function Approximations Package Tutorial)

[1] Hairer, E. and G. Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer, 1991. [2] Iserles, A. and S. P. Nørsett. Order ...

ExpandNumerator (Built-in Mathematica Symbol)

ExpandNumerator[expr] expands out products and powers that appear in the numerator of expr.

EllipticThetaPrime (Built-in Mathematica Symbol)

EllipticThetaPrime[a, u, q] gives the derivative with respect to u of the theta function \[CurlyTheta]_a (u, q) (a = 1, ..., 4).