Hermite; Hess; Hilbert - HP 48gII Advanced User's Reference Manual

Catalog, ...µ
Access:
See also: CASCMD

HERMITE

Type: Function
Description: Returns the nth Hermite polynomial.
Arithmetic, !Þ
Access:
Input: A non-negative integer.
Output: The corresponding polynomial expression.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example: Find the Hermite polynomial with degree 4.
Command:
HERMITE(4)
Result:
16*X^4-48*X^2+12
See also: LEGENDRE, TCHEBYCHEFF

HESS

Type: Command
Description: Returns the Hessian matrix and the gradient of an expression with respect to the specified
variables.
Calculus !Ö
Access:
Input: Level 2/Argument 1: An expression.
Level 1/Argument 2: A vector of the variables.
Output: Level 3/Item 1: The Hessian matrix with respect to the specified variables.
Level 2/Item 2: The gradient with respect to the variables.
Level 1/Item 3: The vector of the variables.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example: Find the Hessian matrix, and the gradient with respect to each variable, of the expression:
Command:
HESS(T^2+2*T*U^2, [T, U])
Result:
{[[2, 2*(2*U)], [2*(2*U), 2*(2*T)]], [2*T+2*U^2, 2*T*(2*U)], [T, U]}
See also: CURL, DIV

HILBERT

Type: Command
Description: Returns a square Hilbert matrix of the specified order.
Matrices, !Ø
Access:
Input: A positive integer, representing the order.
Output: The Hilbert matrix of the specified order.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example: Find the order 3 Hilbert matrix.
Command:
HILBERT(3)
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Computer Algebra Commands 4-37