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 KiB) downloaded 51 time(s).

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...
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.

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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 KiB) downloaded 59 time(s).

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 KiB) downloaded 54 time(s).
gamma_r8.sm (31 KiB) downloaded 48 time(s). <---gamma_r8-2 (function variable revision)

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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 KiB) downloaded 84 time(s).

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 KiB) downloaded 87 time(s).

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 ?

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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 KiB) downloaded 62 time(s).
Gamma [H.T. Davis, Lanczos_overlord].pdf (155 KiB) downloaded 67 time(s).