Summation bug? (HP49G, 50g)

01152015, 01:28 AM
Post: #7




RE: Summation bug? (HP49G, 50g)
(01132015 10:13 PM)Gerson W. Barbosa Wrote: 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. This is the TaylorSeries of \(\arccos(sinc(x))\): \[ \frac{1}{\sqrt{3}}(x\frac{x^3}{90}\frac{x^5}{4200}\frac{x^7}{378000}+\frac{533 x^9}{6286896000}+\frac{2599 x^{11}}{454053600000}+\frac{75799 x^{13}}{572107536000000})+O(x^{14}) \] The correct value is \(\frac{6,286,896,000}{533}=\frac{17,325\cdot9!}{533}\approx11,795,302.0638\) instead of \(32\cdot9! = 11,612,160\). Thus instead of 32 the factor is \(\frac{17,325}{533}\approx32.5047\). Quote:This is a remarkable approximation of the sinc functionNow I hope it's clear why. Cheers Thomas 

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Messages In This Thread 
Summation bug? (HP49G, 50g)  Gerson W. Barbosa  01132015, 07:06 PM
RE: Summation bug? (HP49G, 50g)  Thomas Klemm  01132015, 09:25 PM
RE: Summation bug? (HP49G, 50g)  Gerson W. Barbosa  01132015, 10:13 PM
RE: Summation bug? (HP49G, 50g)  Claudio L.  01132015, 09:40 PM
RE: Summation bug? (HP49G, 50g)  Claudio L.  01132015, 09:54 PM
RE: Summation bug? (HP49G, 50g)  Gerson W. Barbosa  01132015, 10:26 PM
RE: Summation bug? (HP49G, 50g)  Thomas Klemm  01152015 01:28 AM
RE: Summation bug? (HP49G, 50g)  Gerson W. Barbosa  01152015, 09:37 AM

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