Summation bug? (HP-49G, 50g)

[Gerson W. Barbosa]

(01-13-2015 09:25 PM)Thomas Klemm Wrote:  Is this the expression you want to calculate?

\[\cos(\frac{\sqrt{3}}{3}(x+\frac{x^9}{32\cdot9!}-\sum_{k=2}^{4}\frac{x^{2k-1}}{5(2^k-1)(2k-1)!}))\]

(01-13-2015 07:06 PM)Gerson W. Barbosa Wrote:  The HP-48g returns 1 as expected ( cos(0) = 1 ).

That should be the correct result.

I have no idea what happens when using the HP-50g.

Cheers
Thomas

Yes. This is a remarkable approximation of the sinc function, albeit in a limited range:

http://www.wolframalpha.com/input/?i=plo...283%29%2F3

I have no idea why this works, however. Apparently the first four terms are correct. The last term was chosen somewhat arbitrarily to adjust the results to their correct 12 digits.

Interestingly the HP-50g, unlike the HP-48, doesn't handle that summation when x = 0.

Cheers,

Gerson.