16 Point Gaussian Quadrature for the HP-41C/CV/CX (updated)

[Valentin Albillo]

(11-12-2023 05:33 PM)Namir Wrote:  

(11-12-2023 03:24 PM)Valentin Albillo Wrote:  Both values end in 0 ? Really ? It's a 1-in-100 chance. Did you multiply them by 10 as I suggested ? If yes, then they'd be like 6.93... and 9.31... respectively, not the 0.693... and 0.931... values you posted.
Could you please check them out one final time ?

Yes I multiplied both results by 10 ans then moved the decimal to the right, so they correspond to the original answers (now with 10 digits)

Understood, thanks. However, one of your updated coefficients is still in error, namely:

124 6.22535394E-2
125 STO 05

which is missing a digit between the 6^th and 7^th positions. You might want to update it with the correct coefficient.

As a bonus, perhaps you'd like to try your (corrected) program vs. these four integrals and compare your results with the ones provided, which are accurate to all 12 digits shown:

Code:

       / 1
I1 =   |   cos(x)*ln(x) .dx =  -0.946083070367
       / 0

Code:

       / 1
I2 =   |   1/√x .dx =  2.00000000000
       / 0

Code:

       / 1
I3 =   |   Ln(Gamma(x)) .dx =  0.918938533205
       / 0

Code:

       / 1
I4 =   |   1/√(-Ln(x)) .dx =  1.77245385091
       / 0

Regards.
V.