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The Compleat User RPL Encyclopedia


(“Sigma”)

Stack syntax: 'var' start end 'function'
Algebraic syntax: 'Σ(var=start,end,function)'

Not in HP-28

Keyboard Access:
   HP48: RS-TAN
HP49/50: RS-SIN
Summation function, also known as the Sigma function.

The algebraic expression  is displayed in the Equation Writer (and on the stack on the HP49/50 in Textbook Mode) as
This means “The sum of X squared, where X goes from 1 to 1000”.
The stack syntax for the same algebraic expression is:

    
The HP48 always calculates the  function numerically, literally looping from start to end, which can take a long time and cause round-off error accumulation. But it’s useful for small loops.

The HP49/50 in exact mode interprets the  function symbolically, simplifying many summations into much simpler forms. This yields results that are more meaningful, much quicker, and more accurate. It can also handle infinite summations (the HP48 cannot do that).

Examples (for both an HP48 and an HP49/50 in exact mode):

    0.83 seconds on HP50G; 24.4 seconds on HP48GX.
    exactly  in 1.1 seconds on HP50G; the HP48 cannot do this one at all.
BYTES: 2.5