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Community Tip - Did you get an answer that solved your problem? Please mark it as an Accepted Solution so others with the same problem can find the answer easily. X

20-Turquoise

Integral sinc(x)

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.

ACCEPTED SOLUTION

Accepted Solutions
20-Turquoise
(To:-MFra-)
10 REPLIES 10
21-Topaz II
(To:ttokoro)

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.

23-Emerald III
(To:-MFra-)

Maple says:

Luc

23-Emerald III
(To:ttokoro)

Luc

20-Turquoise
(To:LucMeekes)

This is limit of Prime 7.

Therefore, I can't get the results shown by Quora web site.

21-Topaz II
(To:ttokoro)

20-Turquoise
(To:-MFra-)

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.

21-Topaz II
(To:ttokoro)

I use the sinc function according to the definition of the text reported here below. Sin (x) / x is something else ...

20-Turquoise
(To:-MFra-)
23-Emerald III
(To:-MFra-)

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

24-Ruby II
(To:ttokoro)

When I try to solve it (Mathcad 15 F000, Windows 7 x64, 16 GB of RAM), I get an error - "Internal error [1321]":

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