bug#64077: 30.0.50; Wrong definition of gamma function in calc.texi [PATCH]

bug#64077: 30.0.50; Wrong definition of gamma function in calc.texi [PATCH]

[Vladimir Nikishkin]

No Emacs code is affected, but the Gamma Function is defined by a
convergent integral, not a divergent one.

Patch below:

---   doc/misc/calc.texi
@@ -18614,7 +18614,7 @@ Advanced Math Functions
 factorial function:  @samp{gamma(n+1) = fact(n)}.  For general complex
 arguments the gamma function can be defined by the following definite
 integral:
-@texline @math{\Gamma(a) = \int_0^\infty t^{a-1} e^t dt}.
+@texline @math{\Gamma(a) = \int_0^\infty t^{a-1} e^{-t} dt}.
 @infoline @expr{gamma(a) = integ(t^(a-1) exp(t), t, 0, inf)}.
 (The actual implementation uses far more efficient computational methods.)



-- 
Your sincerely,
Vladimir Nikishkin (MiEr, lockywolf)
(Laptop)

bug#64077: 30.0.50; Wrong definition of gamma function in calc.texi [PATCH]

[Eli Zaretskii]

> From: Vladimir Nikishkin <lockywolf@gmail.com>
> Date: Thu, 15 Jun 2023 12:25:04 +0800
> 
> No Emacs code is affected, but the Gamma Function is defined by a
> convergent integral, not a divergent one.
> 
> Patch below:
> 
> ---   doc/misc/calc.texi
> @@ -18614,7 +18614,7 @@ Advanced Math Functions
>  factorial function:  @samp{gamma(n+1) = fact(n)}.  For general complex
>  arguments the gamma function can be defined by the following definite
>  integral:
> -@texline @math{\Gamma(a) = \int_0^\infty t^{a-1} e^t dt}.
> +@texline @math{\Gamma(a) = \int_0^\infty t^{a-1} e^{-t} dt}.
>  @infoline @expr{gamma(a) = integ(t^(a-1) exp(t), t, 0, inf)}.
>  (The actual implementation uses far more efficient computational methods.)

Thanks, fixed.  (But the corresponding @infoline needed to be fixed as
well, right?  So I did that.  And switched to using @sup there, to
produce a nicer HTML output.)

Closing.

bug#64077: 30.0.50; Wrong definition of gamma function in calc.texi [PATCH]

[Andreas Schwab]

On Jun 15 2023, Eli Zaretskii wrote:

>> From: Vladimir Nikishkin <lockywolf@gmail.com>
>> Date: Thu, 15 Jun 2023 12:25:04 +0800
>> 
>> No Emacs code is affected, but the Gamma Function is defined by a
>> convergent integral, not a divergent one.
>> 
>> Patch below:
>> 
>> ---   doc/misc/calc.texi
>> @@ -18614,7 +18614,7 @@ Advanced Math Functions
>>  factorial function:  @samp{gamma(n+1) = fact(n)}.  For general complex
>>  arguments the gamma function can be defined by the following definite
>>  integral:
>> -@texline @math{\Gamma(a) = \int_0^\infty t^{a-1} e^t dt}.
>> +@texline @math{\Gamma(a) = \int_0^\infty t^{a-1} e^{-t} dt}.
>>  @infoline @expr{gamma(a) = integ(t^(a-1) exp(t), t, 0, inf)}.
>>  (The actual implementation uses far more efficient computational methods.)
>
> Thanks, fixed.  (But the corresponding @infoline needed to be fixed as
> well, right?  So I did that.  And switched to using @sup there, to
> produce a nicer HTML output.)

Using @sup{..} is wrong here, though.  The @infoline line is using calc
algebraic syntax.

-- 
Andreas Schwab, SUSE Labs, schwab@suse.de
GPG Key fingerprint = 0196 BAD8 1CE9 1970 F4BE  1748 E4D4 88E3 0EEA B9D7
"And now for something completely different."

bug#64077: 30.0.50; Wrong definition of gamma function in calc.texi [PATCH]

[Eli Zaretskii]

> From: Andreas Schwab <schwab@suse.de>
> Cc: eliz@gnu.org,  lockywolf@gmail.com
> Date: Thu, 15 Jun 2023 09:54:26 +0200
> 
> On Jun 15 2023, Eli Zaretskii wrote:
> 
> > Thanks, fixed.  (But the corresponding @infoline needed to be fixed as
> > well, right?  So I did that.  And switched to using @sup there, to
> > produce a nicer HTML output.)
> 
> Using @sup{..} is wrong here, though.  The @infoline line is using calc
> algebraic syntax.

I don't see how that follows.  Those look like function definitions to
me, and they are not inside @kbd (which would indicate something the
user should type into Calc).

So I don't think @sup is wrong there.

bug#64077: 30.0.50; Wrong definition of gamma function in calc.texi [PATCH]

[Andreas Schwab]

On Jun 15 2023, Eli Zaretskii wrote:

> I don't see how that follows.  Those look like function definitions to
> me, and they are not inside @kbd (which would indicate something the
> user should type into Calc).

Exactly, in algrebraic notion.  This is a TeX-like notation that uses
the literal characters ^ and _.

> So I don't think @sup is wrong there.

exp is a function, not a variable.

-- 
Andreas Schwab, SUSE Labs, schwab@suse.de
GPG Key fingerprint = 0196 BAD8 1CE9 1970 F4BE  1748 E4D4 88E3 0EEA B9D7
"And now for something completely different."

bug#64077: 30.0.50; Wrong definition of gamma function in calc.texi [PATCH]

[Eli Zaretskii]

> From: Andreas Schwab <schwab@suse.de>
> Cc: lockywolf@gmail.com,  64077@debbugs.gnu.org
> Date: Thu, 15 Jun 2023 10:16:14 +0200
> 
> exp is a function, not a variable.

Fixed, thanks.