The Museum of HP Calculators

HP Forum Archive 20

 Summing FunctionMessage #1 Posted by Jim Yohe on 27 Mar 2011, 9:08 p.m. Is there a similar function to the HP-27S Summing {sigma} Function (page 108 of Owner's Manual) but available on the HP-42S or the HP-32SII and in the related owner's manual(s)? I can't seem to find one but I could have overlooked it. FYI, from HP-27S manual: {sigma}(counter variable : starting value : ending value : step size : algebraic expression) Definition: Sums values of the algebraic expression for values of the counter variable. The counter variable starts with the starting value and is incremented in steps to a final ending value. I'd like to try out the following equation in SOLVE on my 42S and 32SII if possible. Solve for PI' (since PI is already a function): PI'=(6÷SQRT(3))*{sigma}(I:0:LAST:1:(-1)^I÷((2xI+1)x3^I)) It takes a value of 21 in variable LAST to produce 12 digits of accuracy (last digit rounded up) for PI'. Ref: The history of the approximation of the number PI; 4.1. Gottfried Wilhelm Leibniz (1646-1716); Scholz, Werner; http://cwscholz.net/projects/fba/fba.html === Confounded ... how, if even possible, do I embed special characters like the {sigma} symbol (Σ) into a forum message? :-/

 Re: Summing FunctionMessage #2 Posted by Don Shepherd on 27 Mar 2011, 9:30 p.m.,in response to message #1 by Jim Yohe There is no sigma command in the 32sii solver, but you could do it in a program. This gives you the sigma character in a forum post (thanks Thomas Klemm): [img:http://www.hpmuseum.org/software/symsums.gif]

 Re: Summing FunctionMessage #3 Posted by Jim Yohe on 27 Mar 2011, 9:40 p.m.,in response to message #2 by Don Shepherd Yes, thank you Thomas (and Don). Too bad I didn't know it earlier, but better late than never. PI'=(6÷SQRT(3))*(I:0:LAST:1:(-1)^I÷((2xI+1)x3^I)) That looks better! Edited: 27 Mar 2011, 10:52 p.m.

 Re: Summing FunctionMessage #4 Posted by Thomas Klemm on 29 Mar 2011, 2:18 a.m.,in response to message #2 by Don Shepherd You might like to read my article: How to use a formula in a post . Here's the formula in LaTeX: \frac{\pi}{6}=\frac{1}{\sqrt{3}}\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)3^n} At that's the result: $\frac{\pi}{6}=\frac{1}{\sqrt{3}}\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)3^n}$ Quote: you could do it in a program 00 { 42-Byte Prgm } 01>LBL "Leibniz" 02 STO 00 03 SIGN 04 ENTER 05 ENTER 06 LBL 00 07 X<> ST Z 08 2 09 + 10 X<>Y 11 -3 12 / 13 ENTER 14 RCL/ ST Z 15 R^ 16 + 17 DSE 00 18 GTO 00 19 3 20 SQRT 21 * 22 STO+ ST X 23 END Run: 21 XEQ "Leibniz" Kind regards Thomas Edited: 29 Mar 2011, 2:24 a.m.

 Re: Summing FunctionMessage #5 Posted by Jim Yohe on 29 Mar 2011, 3:24 a.m.,in response to message #4 by Thomas Klemm Thomas, that looks even better but it's not the why it looks when the equation is entered into the HP-27S, but thank you non-the-less. I'll have to practice playing around with LaTeX a bit in between my studies. So much to do ... so little time. :-) Thanks for the HP-42S program, as well.

 Re: Summing FunctionMessage #6 Posted by Martin Pinckney on 29 Mar 2011, 9:10 a.m.,in response to message #5 by Jim Yohe Quote: Thomas, that looks even better but it's not the why it looks when the equation is entered into the HP-27S... $\frac{\pi}{6}=\frac{1}{\sqrt{3}}\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)3^n}$ Jim, if you want to see something like the above, you'll need a 48GX ;-)

 Re: Summing FunctionMessage #7 Posted by Jim Yohe on 29 Mar 2011, 1:37 p.m.,in response to message #6 by Martin Pinckney That's nice to know and I will be able to see that for myself when I become the owner of a 48GX soon. :-D Though my main question was whether the 42s and 32sii had a similar "summing function" as the 27s since I failed find one in either of the owner's manuals. Don directly answered my question for the 32sii and I'd assume the 42s doesn't provide that same function either with Thomas' indirect answer of a programming solution. Obviously you can do so much more through programming than relying on build in "functions" and I'm content with that. Thank you all.

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