# Series; Seval - HP 48gII Advanced User's Reference Manual

Graphing calculator.

row reduction is done without reducing the last column, but the last column will be modified
by the reduction of the rest of the matrix.
Example:
Reduce to row-reduced echelon form, modulo 3, the matrix:
2 1
3 4
Command:
rref[[2,1][3,4]]
Result:
[[-1,0][0,1]]
rref

## SERIES

Type:
Command
Description:
For a given function, computes Taylor series, asymptotic development and limit at finite or
infinite points.
Calculus, P
Access:
Input:
Level 3/Argument 1: The function f(x)
Level 2/Argument 2: The variable if the limit point is 0, or an equation x = a if the limit point
is a. If the function is in terms of the current variable, this can be given as just the value a.
Level 1/Argument 3: The order for the series expansion. The minimum value is 2, and the
maximum value is 20.
Output:
Level 2/Item 1: A list containing the limit as a value and as the equivalent expression, an
expression approximating the function near the limit point, and the order of the remainder.
These are expressed in terms of a small parameter h.
Level 1/Item 2: An expression for h in terms of the original variable.
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:
Obtain the second order Taylor series expansion of ln(x) at x=1.
Command:
SERIES(LN(X),1,2)
Result:
{{Limit: 0, Equiv: h, Expans: -1/2*h^2+h, Remain: h^3}, h=X- 1}
TAYLOR0

### SEVAL

Type:
Function
Description:
Simplifies the given expression. Simplifies the expression except at the highest level, and also
evaluates any existing variables that the expression contains and substitutes these back into
the expression.
Catalog, ...µ
Access:
Input:
Level 1/Argument 1: An algebraic expression.
Output:
The expression simplified and with existing variables evaluated.
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:
With π stored in the variable Y, and the variables X and Z not in the current path, simplify the
following expression. Note that the top-level simplification is not carried out.
Sin(3x – y + 2z – (2x – z)) – Sin(x – 2y + (y + 3z))
4-64 Computer Algebra Commands
, or Limits and series, !Ö
CALC
&
LIMITS
SERIES