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Vaclav Kotesovec
Vaclav Kotesovec
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Bug introduced in 7.0 and fixed in 10.2.0

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://members.chello.cz/kotesovec/math_articles/kotesovec_too_many_errors_A002720.pdfhttp://www.kotesovec.cz/math_articles/kotesovec_too_many_errors_A002720.pdf

A same result we get with Hypergeometric1F1[-n,1,-1] = LaguerreL[n,-1]

Bug introduced in 7.0 and fixed in 10.2.0

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://members.chello.cz/kotesovec/math_articles/kotesovec_too_many_errors_A002720.pdf

A same result we get with Hypergeometric1F1[-n,1,-1] = LaguerreL[n,-1]

Bug introduced in 7.0 and fixed in 10.2.0

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://www.kotesovec.cz/math_articles/kotesovec_too_many_errors_A002720.pdf

A same result we get with Hypergeometric1F1[-n,1,-1] = LaguerreL[n,-1]

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ilian
ilian
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Bug introduced in 7.0 and fixed in 10.2.0

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://members.chello.cz/kotesovec/math_articles/kotesovec_too_many_errors_A002720.pdf

A same result we get with Hypergeometric1F1[-n,1,-1] = LaguerreL[n,-1]

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://members.chello.cz/kotesovec/math_articles/kotesovec_too_many_errors_A002720.pdf

A same result we get with Hypergeometric1F1[-n,1,-1] = LaguerreL[n,-1]

Bug introduced in 7.0 and fixed in 10.2.0

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://members.chello.cz/kotesovec/math_articles/kotesovec_too_many_errors_A002720.pdf

A same result we get with Hypergeometric1F1[-n,1,-1] = LaguerreL[n,-1]

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Vaclav Kotesovec
Vaclav Kotesovec
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Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://members.chello.cz/kotesovec/math_articles/kotesovec_too_many_errors_A002720.pdf

A same result we get with Hypergeometric1F1[-n,1,-1] = LaguerreL[n,-1]

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://members.chello.cz/kotesovec/math_articles/kotesovec_too_many_errors_A002720.pdf

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞]

Mathematica (wrong) output

13/16 = 0.8125

The right result is:

31/48 = 0.645833...

But numerically it is computed right (after ~ 1 hour):

N[Table[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], {n, 1000000, 10000000, 1000000}], 20] 
{0.64595327485857865704, 0.64591815870538845793, 0.64590259799022250717, 
 0.64589332088298149047, 0.64588698941420000820, 0.64588231547803760347, 0.64587868275613942973, 0.64587575441366589107, 0.64587332876408306831, 0.64587127669377150813}

I already reported this bug in 2012, but still was not fixed (in versions 7,8,9,10) http://code.google.com/p/mathematica/issues/list see Issue 46

For more please see my article "Too many errors around coefficient C1 in asymptotic of sequence A002720" http://members.chello.cz/kotesovec/math_articles/kotesovec_too_many_errors_A002720.pdf

A same result we get with Hypergeometric1F1[-n,1,-1] = LaguerreL[n,-1]

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