example you could define $=1_? Then other currencies could be defined as multiples or fractions of 1_? The calculator has symbols for Yen, Pounds and Euros; other currencies could be defined using their names. The unit conversion system would then check conversions between them for consistency because ? is recognized as a base unit.

Access: Catalog, …µ, or ~…3

∞(Infinity)

Type: Function

Description: Infinity: used to signify a numeric result that is infinite by the rules of arithmetic, such as the result of dividing a non-zero number by zero. The calculator recognizes two kinds of infinity: signed and unsigned. Evaluating '1/0' gives an unsigned infinity '∞'. Selecting infinity from the keyboard,

from the CHARS table, or from the catalog …µreturns '+∞' and the sign can be changed. Calculations with the unsigned infinity return unsigned infinity or ? as their result. Calculations with the signed infinity can return ordinary numeric results, as in the example. Positive infinity and unsigned infinity are equal if tested with ==, but are not identical if tested with SAME.

Access: Keyboard, CHARS, or catalog, …µ

Flags: Exact mode must be set (flag –105 clear),

and numeric mode must not be set (flag –3 clear) for mathematical operations to give ∞ as a result, and for executing ∞ from the keyboard or catalog to give +∞ and not an error.

Example: Find the arc tangent of minus infinity. Assume that radians mode is set. Command: ATAN(-∞)

Results: -(π/2)

Σ(Summation)

Type: Function

Description: Summation Function: Calculates the value of a finite series.

The summand argument smnd can be a real number, a complex number, a unit object, a local or global name, or an algebraic object. The algebraic syntax for Σ differs from the stack syntax. The algebraic syntax is: 'Σ(index=initial,final,summand)'

Access:

…½

 

(½is the right-shift of the Skey).

Flags:

Symbolic Constants (–2), Numerical Results (–3)

 

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L4/A1

L3/A2

L2/A3

L1/A4

 

L1/I1

 

 

 

 

 

 

 

 

 

 

'indx'

xinit

xfinal

smnd

→

xsum

 

 

'indx'

'init'

x

final

smnd

→

'Σ(indx = init, x , smnd)'

 

 

 

 

 

 

final

 

 

'indx'

xinit

'final'

smnd

→

'Σ(indx = xinit, final, smnd)'

 

 

'indx'

'init'

'final'

smnd

→

'Σ(indx = init, final, smnd)'

 

 

 

 

 

 

 

 

 

 

L = Level; A = Argument; I = Item

 

 

 

Example:

The command sequence 'N' 1 5 'A^N' Σ

returns

 

 

 

'(EXP(6*LN(A))-A)/(A-1)'.

 

 

 

See also:

TAYLR, ∫, ∂

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Σ+

(Sigma Plus)

Type:

 

Command

Description:

Sigma Plus Command: Adds one or more data points to the current statistics matrix (reserved

 

 

variable ΣDAT).

 

 

For a statistics matrix with m columns, arguments for Σ+ can be entered several ways:

Full Command and Function Reference 3-289