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Feb 12, 2024, 9:53:38 AMFeb 12

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There is discussion about this on mathoverlow [1]:

The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear

correct and it contradicts numerical computations, including verification

with mpmath.

Session:

sage: import mpmath

sage: su4=sum(1/factorial(n**2),n,1,oo);su4

hypergeometric((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)

sage: CC(su4)

1.17227289255719 - 7.88860905221012e-31*I

sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)

mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')

sage: su5=sum(1/factorial(i**2) for i in range(1,100))

sage: CC(su5)

1.04166942239864

sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])

mpf('1.0416694223986369')

[1]: https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu

The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear

correct and it contradicts numerical computations, including verification

with mpmath.

Session:

sage: import mpmath

sage: su4=sum(1/factorial(n**2),n,1,oo);su4

hypergeometric((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)

sage: CC(su4)

1.17227289255719 - 7.88860905221012e-31*I

sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)

mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')

sage: su5=sum(1/factorial(i**2) for i in range(1,100))

sage: CC(su5)

1.04166942239864

sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])

mpf('1.0416694223986369')

[1]: https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu

Feb 14, 2024, 12:52:30 PMFeb 14

to sage-...@googlegroups.com, Nils Bruin

It appears to come from Maxima, but I have trouble reproducing this in Maxima.

Perhaps it's a bug in the Maxima interface?

Is there a direct way to see how Maxima is called in this instance?

Dima

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Feb 14, 2024, 1:12:53 PMFeb 14

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Maxima's simplify_sum function produces something similar looking:

(%i4) load("simplify_sum");

(%o4) "/usr/share/maxima/5.45.1/share/solve_rec/simplify_sum.mac"

(%i5) sum(1/factorial(n^2), n, 1, inf), simpsum;

(%o5) 'sum(1/(n^2)!,n,1,inf)

(%i6) simplify_sum(%);

1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum

1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum

(%o6) %f[1,4]([1],[1-%i,%i+1,1-sqrt(2)*%i,sqrt(2)*%i+1],1)

--

Oscar

> To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq2hSxdzoiaNvOLPCur3_AB1-mpPjsMFhdurTcUrz31T9Q%40mail.gmail.com.

(%i4) load("simplify_sum");

(%o4) "/usr/share/maxima/5.45.1/share/solve_rec/simplify_sum.mac"

(%i5) sum(1/factorial(n^2), n, 1, inf), simpsum;

(%o5) 'sum(1/(n^2)!,n,1,inf)

(%i6) simplify_sum(%);

1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum

1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum

(%o6) %f[1,4]([1],[1-%i,%i+1,1-sqrt(2)*%i,sqrt(2)*%i+1],1)

--

Oscar

Feb 14, 2024, 2:14:36 PMFeb 14

to sage-...@googlegroups.com

On Wed, Feb 14, 2024 at 6:12 PM Oscar Benjamin <oscar.j....@gmail.com> wrote:

Maxima's simplify_sum function produces something similar looking:

(%i4) load("simplify_sum");

(%o4) "/usr/share/maxima/5.45.1/share/solve_rec/simplify_sum.mac"

(%i5) sum(1/factorial(n^2), n, 1, inf), simpsum;

(%o5) 'sum(1/(n^2)!,n,1,inf)

(%i6) simplify_sum(%);

Oh, I see - I missed an explicit call to simplify_sum.

1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum

1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum

(%o6) %f[1,4]([1],[1-%i,%i+1,1-sqrt(2)*%i,sqrt(2)*%i+1],1)

It seems to be a bug in simplify_sum() - nusum can't do it ( "non-rational term ratio to nusum")

indeed, it's obvious that the sum is not hypergeometric, as the consequent terms ratio is not of the right type,

so it does try something more clever - but fails.

Dima

To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAHVvXxTJNfBgjtjFCZJcd6rjizPVDn9bc7rhjS0FoTwd5tJ46g%40mail.gmail.com.

Feb 14, 2024, 7:27:47 PMFeb 14

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I've filed https://sourceforge.net/p/maxima/bugs/4262/

Apr 26, 2024, 9:24:27 AMApr 26

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On Thu, Feb 15, 2024 at 2:27 AM Dima Pasechnik <dim...@gmail.com> wrote:

>

> I've filed https://sourceforge.net/p/maxima/bugs/4262/

>

Is maxima supported?
>

> I've filed https://sourceforge.net/p/maxima/bugs/4262/

>

There is no progress on their bug system for more than 2 months.

SEGV is not pleasant, but incorrect symbolic result casts doubts about

all symbolic sage computations, especially those that can't be

verified numerically.

Apr 26, 2024, 2:29:42 PMApr 26

to sage-...@googlegroups.com

On Fri, Apr 26, 2024 at 2:24 PM Georgi Guninski <ggun...@gmail.com> wrote:

>

> On Thu, Feb 15, 2024 at 2:27 AM Dima Pasechnik <dim...@gmail.com> wrote:

> >

> > I've filed https://sourceforge.net/p/maxima/bugs/4262/

> >

>

> Is maxima supported?

> There is no progress on their bug system for more than 2 months.

not many people are involved, and some bugs stay open for years there.
>

> On Thu, Feb 15, 2024 at 2:27 AM Dima Pasechnik <dim...@gmail.com> wrote:

> >

> > I've filed https://sourceforge.net/p/maxima/bugs/4262/

> >

>

> Is maxima supported?

> There is no progress on their bug system for more than 2 months.

> SEGV is not pleasant, but incorrect symbolic result casts doubts about

> all symbolic sage computations, especially those that can't be

> verified numerically.

>

> --

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