Download HolonomicFunctions (User's Guide)

Out[62]=
{1, Dx }
DFinitePlus[Annihilator[LegendreP[n + 1, x], {S[n], Der[x]}],
Annihilator[LegendreP[n, x], {S[n], Der[x]}]]
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2
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Out[63]= {(2n + 2)Sn Dx + (1 − x )Dx + (−2nx − 4x)Dx + (−n − 3n − 2),
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2
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(2n +12n +22n+12)Sn +(−x +2x −1)Dx +(−4n x−20n2 x−32nx−16x)Sn
+ (−2nx3 + 2nx − 4x3 + 4x)Dx + (2n3 − n2 x2 + 9n2 − 3nx2 + 13n − 2x2 + 6),
(x4 − 2x2 + 1)Dx3 + (4x3 − 4x)Dx2 + (2n3 + 8n2 + 10n + 4)Sn
+ (−3n2 x2 + 3n2 − 7nx2 + 7n − 2x2 + 2)Dx + (−2n3 x − 8n2 x − 10nx − 4x)}
In[63]:=
In[64]:=
Out[64]=
UnderTheStaircase[%]
{1, Dx , Sn , Dx2 }
Sometimes the dimension can even drop:
In[65]:=
Out[65]=
In[66]:=
Out[66]=
O
ann = Annihilator[HarmonicNumber[n], S[n]]
{(n + 2)Sn2 + (−2n − 3)Sn + (n + 1)}
DFiniteOreAction[ann, S[n] − 1]
{(n + 2)Sn + (−n − 1)}
See Also
Annihilator, DFinitePlus, DFiniteSubstitute, DFiniteTimes
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