Airy functions

[someone]

Hi,

Just for general information: today I started working
on implementing the Airy functions. I hope to provide
first results soon.

[Tom Bachmann]

Awesome, keep it coming!

[someone]

Hi Tom,

> Awesome, keep it coming!

Just see my "airy" branch for a first very limited version.
(Only known special values, limits and differentiation.)

[someone]

What names should the Airy functions get in sympy?
The following list shows what other CAS and similar
software does:

Maxima:

airy_ai(...)
airy_dai(...)

Sage:

airy_ai(...)
airy_ai_prime(...)

mpmath:

airyai(...)
No primed functions?

Octave:

airy(k, ...)
with k = (1,2,3,4) and 0 mens Ai(Z), 1 means dAi(Z)/dZ etc

Mathematica:

AiryAi[...]
AiryAiPrime[...]

Maple:

AiryAi(...)
AiryAi(n, ...) for the primed version

[Fredrik Johansson]

On Fri, May 11, 2012 at 3:16 PM, someone <some...@bluewin.ch> wrote:
> What names should the Airy functions get in sympy?
> The following list shows what other CAS and similar
> software does:
>
> Maxima:
>
>   airy_ai(...)
>   airy_dai(...)
>
> Sage:
>
>   airy_ai(...)
>   airy_ai_prime(...)
>
> mpmath:
>
>   airyai(...)
>   No primed functions?

airyai(..., derivative=k) for the kth derivative

Fredrik

[Tom Bachmann]

Since we generally follow mpmath conventions, I would suggest airyai(z,
k=0) and airybi(z, k=0) until someone comes up with a particular
argument against it.

[Aaron Meurer]

Following mpmath conventions is a good idea, and I like airyai better
anyway. Regardless of what we do, I think we should use the notation
that puts the derivative as one of the arguments rather than have a
separate airy_prime function.

Aaron Meurer

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[someone]

> Following mpmath conventions is a good idea, and I like airyai better
> anyway.

Ok. This is consistent with the Fresnels where we removed the "_" too.

> Regardless of what we do, I think we should use the notation
> that puts the derivative as one of the arguments rather than have a
> separate airy_prime function.

I vote against this for mainly two reasons:

- All formula become more complicated to read and write
and we make the Airy function essentially a 2-Argument
function.

- All other major CAS do provide separate functions
which are also standard mathemtical notation.
(Hence users may expect these functions. For example
I overlooked the implementation of mpmath ;-))

Maybe there are even more reasons to do this, but these
two come to my mind right now.

You are right, for mathematical reasons we would not need
extra functions. We even could write an unevaluated derivative.
(Which in turn gives problems to express the second derivative
which should simplify to Airys again.) For the same reasons
we could express cos by sin or right away by exp.

[someone]

> > mpmath:
> >
> >   airyai(...)
> >   No primed functions?
>
> airyai(..., derivative=k) for the kth derivative

Ok, thanks. Didn't look close enough.