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Quora shows interesting math. Prime 7 can show third equation is also pi.
I want to calculate until
and
does not show pi/2
need very long time to solve.
Solved! Go to Solution.
Please note that the definition of Mathcad's sinc function differs from that used elsewhere. The Mathcad definition is sinc(x) = sin(x)/x, while on certain texts it is defined like this: sinc(x) = sin(πx) / (πx) so in the comparison of the calculated values and those of the text there may be differences. I'm referring to Mathcad 15. Certain errors in MC15 have been fixed in Prime 7.
Maple says:
Luc
Luc
This is limit of Prime 7.
Therefore, I can't get the results shown by Quora web site.
TOL=10^-3
TOL=10^-7
Therefore, Quora and Luc show the answer is pi/2 for n=0 to 6. But n>6 are not calculate symbolically when using 15 digit accuracy. May be n>6 also show pi/2 symbolically when calculate more digit accuracy. Or Quora is true mathematically.
I use the sinc function according to the definition of the text reported here below. Sin (x) / x is something else ...
The sinc function is not included in the ISO standard for mathematical functions, ISO 80000-2:2013, nor in its 2019 update.
The 'NIST Handbook of mathematical functions' defines the Sinc function:
(but that's not the sinc function...)
There's a difference between the sinc function and the normalised sinc function according to Wikipedia. Follow the link to Rayleigh's formula to find how it was originally defined...
Success!
Luc
When I try to solve it (Mathcad 15 F000, Windows 7 x64, 16 GB of RAM), I get an error - "Internal error [1321]":