21-Topaz I

Solved

Integral sinc(x)

Forum|Forum|4 years ago
October 2, 2021
4 replies
6134 views

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.

Mathcad Usage

Best answer by ttokoro

Borwein integral - Wikipedia

Quora is true.

-

-MFra-

21-Topaz II

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.

answer to ttokoro.jpg

L

LucMeekes

23-Emerald IV

Maple says:

Luc

L

LucMeekes

23-Emerald IV

Luc

ttokoro

Author

21-Topaz I

This is limit of Prime 7.

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

t.t.

-

-MFra-

21-Topaz II

answer to ttokoro 1.jpg

ttokoro

Author

21-Topaz I

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.

t.t.