Sanity checked vs Mathcad 11.
Cuts the mustard a bit finer than first version.
Γ(1,0)="Uncertainty" unsolved.

Wrote

Sanity checked vs Mathcad 11.
Cuts the mustard a bit finer than first version.
Γ(1,0)="Uncertainty" unsolved.

There is no uncertainty in gamma_r6.
Everything look correct with those numbers.

Γ(1)=1
γ(1,0)=0
Γ(1,0)=1

1. Example 3 ... added
2. Uncertainty solved for version not having 0 defined.

Gamma [overlord sr.6].sm (39,32 KiB) scaricato 1205 volta(e).

Wrote

...
3. don't want to disrespect, Alvaro's is a single line awesome code.
4. mine has same algorithm with more features, with faster calculation.
...

Hi overlord, of course you don't. My codes are mostly pedagogical, not for optimized for speed nor accuracy or something else. It's good to have codes with that.

Best regards.
Alvaro.

Wrote

Hi overlord, of course you don't. My codes are mostly pedagogical, not for optimized for speed nor accuracy or something else. It's good to have codes with that.

Best regards.
Alvaro.

Thanks, inspired by your code using sum(), and eliminating some useless variable definitions;
I have managed to speed up 30% percent under linux. And should be more precise now.
Only the 15th decimal digit may differs, and this is only sometimes.

Regards.

gamma_r7.sm (28,8 KiB) scaricato 1506 volta(e).

Apparently solve() can't read product() too.
Had to change algorithm style for incomplete function.
Hopefully this is the last version.
Well, I have my doubts... (swh)

Regards

PS: solvers may not found an answer just because variable names, Razonar's idea implemented.

gamma_r8.sm (29,61 KiB) scaricato 1508 volta(e).
gamma_r8.sm (31,51 KiB) scaricato 1531 volta(e). <---gamma_r8-2 (function variable revision)

Wrote

Wrote

Hi overlord, of course you don't. My codes are mostly pedagogical, not for optimized for speed nor accuracy or something else. It's good to have codes with that.

Best regards.
Alvaro.

Thanks, inspired by your code using sum(), and eliminating some useless variable definitions;
I have managed to speed up 30% percent under linux. And should be more precise now.
Only the 15th decimal digit may differs, and this is only sometimes.

Regards.

The algorithm is valid for Re(z) > 0. See this notes please.

gamma.sm (27,93 KiB) scaricato 1970 volta(e).

Best regards.
Alvaro.

Wrote

Hopefully this is the last version.
Well, I have my doubts... (swh)

Can't be more right !
1. Smath Lanczos Davide code is 1/1 Keisan, Mathcad 11.
2. It supports imaginary argument.
3. It supports RootSecant.
4. Confirmed, your last Lanczos does not support RootSecant.
I haven't checked Alvaro suggestion.

... just a remark:
Mathsoft suggested use exp(,) instead of e^.
exp(,) more accurate/faster at kernel level.

Imaginary numbers supplicated.
Root Secant better than HT Davis. (last digit)
Graphing works for all functions.
Usually all solve methods works.

Regards

gamma_r9.sm (36,93 KiB) scaricato 1918 volta(e).

Your latest sr.9 is mostly red in SS 6179, takes Eternity.
Who cares ^308 ?
On the other hand, could be damned slow in practical applications.
Because not being built-in in native Smath ... proof:
Lanczos plots Hypergeometric but takes 1 min versus resident Gamma(x).
Why not use Lanczos as given by Davide ?

Wrote

Your latest sr.9 is mostly red in SS 6179, takes Eternity.
Who cares ^308 ?
On the other hand, could be damned slow in practical applications.
Because not being built-in in native Smath ... proof:
Lanczos plots Hypergeometric but takes 1 min versus resident Gamma(x).
Why not use Lanczos as given by Davide ?

- Who cares SMath 6179?
- My algorithm is faster than your examples.
- My Γ(x) prints hypergeom in less than a second, don't need integrated Gamma().
- Because my function has more features, and faster.

Your PC is slow, your SMath_6179 is slow and broken, your examples are slow.

Gamma [H.T. Davis, Lanczos_overlord].sm (62,36 KiB) scaricato 1387 volta(e).
Gamma [H.T. Davis, Lanczos_overlord].pdf (155,73 KiB) scaricato 822 volta(e).