# Ldec; Legendre - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Input:
Level 3/Argument 1: The number of rows you want in the resulting matrix.
Level 2/Argument 2: The number of columns you want in the resulting matrix.
Level 1/Argument 3: A program that uses two arguments. An expression with the two
variables I, J can be used instead.
Output:
The resulting matrix.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Build a 2 × 3 matrix with a
Command:
LCXM(2,3,«
3 5 7
4 6 8
Result:

## LDEC

Type:
Command
Description:
Solves a linear differential equation with constant coefficients, or a system of first order linear
differential equations with constant coefficients.
Symbolic solve, !Îor P
Access:
Input:
Level 2/Argument 1: For a single equation, the function forming the right hand side of the
equation. For a system of equations, an array comprising the terms not containing the
dependent variables.
Level 1/Argument 2: For one equation, the auxiliary polynomial. For a system of equations,
the matrix of coefficients of the dependent variables.
Output:
The solution.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Solve 2sin(x), with the auxiliary polynomial x
Command:
LDEC(2*SIN(X),X^2+1)
Result:
COS(X)*(cC0 -X)+(cC1 — -1)*SIN(X)
DESOLVE

### LEGENDRE

Type:
Function
Description:
Returns the nth degree Legendre polynomial.
Arithmetic, !Þ
Access:
Input:
An integer, n.
Output:
The nth Legendre polynomial.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Find the Legendre polynomial with degree 4.
Command:
LEGENDRE(4)
Result:
(35*X^4-30*X^2+3)/8
HERMITE, TCHEBYCHEFF
=i+2j.
ij
I J 'I+2*J'")
SOLVER
LL
POLYNOMIAL
or !Ö
DIFF
+1:
2
Computer Algebra Commands 4-47