n-th derivative of an arbitrary polynomial / power seriesCompose two special power series expansionsSymbolic linear algebra gradients/matrix calculusPartial derivative: Understanding outputterm derivationSimplify sum of unnatural conditional functions generated by derivativeTaking derivative of general orderRelations between two reciprocal partial derivatives?
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n-th derivative of an arbitrary polynomial / power series
Compose two special power series expansionsSymbolic linear algebra gradients/matrix calculusPartial derivative: Understanding outputterm derivationSimplify sum of unnatural conditional functions generated by derivativeTaking derivative of general orderRelations between two reciprocal partial derivatives?
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How can I tell mathematica to give me the symbolic derivative of the following sum
$$ fracpartial^npartial x^nsum_j=0^Ngamma_jx^j=sum_j=n^Nfracj!(j-n)! gamma_jx^j-n $$
I only get the left hand side with my simple but wrong code:
G=Sum[Subscript[[Gamma], i]*(x)^i, i, 0, N]
Assuming[n <= N, D[G, x, n]
Quick followup question: How do I get $gamma_nn!$ for x=0?
calculus-and-analysis symbolic polynomials
asked 8 hours ago
the.polothe.polo
1112 bronze badges
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the.polo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$begingroup$
How can I tell mathematica to give me the symbolic derivative of the following sum
$$ fracpartial^npartial x^nsum_j=0^Ngamma_jx^j=sum_j=n^Nfracj!(j-n)! gamma_jx^j-n $$
I only get the left hand side with my simple but wrong code:
G=Sum[Subscript[[Gamma], i]*(x)^i, i, 0, N]
Assuming[n <= N, D[G, x, n]
Quick followup question: How do I get $gamma_nn!$ for x=0?
calculus-and-analysis symbolic polynomials
asked 8 hours ago
the.polothe.polo
1112 bronze badges
New contributor
the.polo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment
|
$begingroup$
How can I tell mathematica to give me the symbolic derivative of the following sum
$$ fracpartial^npartial x^nsum_j=0^Ngamma_jx^j=sum_j=n^Nfracj!(j-n)! gamma_jx^j-n $$
I only get the left hand side with my simple but wrong code:
G=Sum[Subscript[[Gamma], i]*(x)^i, i, 0, N]
Assuming[n <= N, D[G, x, n]
Quick followup question: How do I get $gamma_nn!$ for x=0?
calculus-and-analysis symbolic polynomials
asked 8 hours ago
the.polothe.polo
1112 bronze badges
New contributor
the.polo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
How can I tell mathematica to give me the symbolic derivative of the following sum
$$ fracpartial^npartial x^nsum_j=0^Ngamma_jx^j=sum_j=n^Nfracj!(j-n)! gamma_jx^j-n $$
I only get the left hand side with my simple but wrong code:
G=Sum[Subscript[[Gamma], i]*(x)^i, i, 0, N]
Assuming[n <= N, D[G, x, n]
Quick followup question: How do I get $gamma_nn!$ for x=0?
calculus-and-analysis symbolic polynomials
calculus-and-analysis symbolic polynomials
asked 8 hours ago
the.polothe.polo
1112 bronze badges
New contributor
the.polo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
the.polothe.polo
1112 bronze badges
New contributor
the.polo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
the.polothe.polo
1112 bronze badges
New contributor
the.polo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
the.polothe.polo
1112 bronze badges
asked 8 hours ago
the.polothe.polo
1112 bronze badges
1112 bronze badges
New contributor
the.polo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
the.polo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment
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1 Answer
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$begingroup$
Clear["Global`*"]
rule = D[Sum[expr_, k_Symbol, kmin_, kmax_], x_, n_] :>
Sum[D[expr, x, n], k, kmin, kmax];
Format[γ[j_]] := Subscript[γ, j]
expr = Sum[γ[j] x^j, j, 0, n];
(expr2 = D[expr, x, n] /. rule) // TraditionalForm
where FactorialPower is used and expr2 equivalent to
TraditionalForm[
expr3 = ReplacePart[expr2, 1 -> FunctionExpand[expr2[[1]]]] /.
Gamma[z_] :> (z - 1)!]
answered 7 hours ago
Bob HanlonBob Hanlon
66.2k3 gold badges37 silver badges102 bronze badges
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Clear["Global`*"]
rule = D[Sum[expr_, k_Symbol, kmin_, kmax_], x_, n_] :>
Sum[D[expr, x, n], k, kmin, kmax];
Format[γ[j_]] := Subscript[γ, j]
expr = Sum[γ[j] x^j, j, 0, n];
(expr2 = D[expr, x, n] /. rule) // TraditionalForm
where FactorialPower is used and expr2 equivalent to
TraditionalForm[
expr3 = ReplacePart[expr2, 1 -> FunctionExpand[expr2[[1]]]] /.
Gamma[z_] :> (z - 1)!]
answered 7 hours ago
Bob HanlonBob Hanlon
66.2k3 gold badges37 silver badges102 bronze badges
$endgroup$
add a comment
|
$begingroup$
Clear["Global`*"]
rule = D[Sum[expr_, k_Symbol, kmin_, kmax_], x_, n_] :>
Sum[D[expr, x, n], k, kmin, kmax];
Format[γ[j_]] := Subscript[γ, j]
expr = Sum[γ[j] x^j, j, 0, n];
(expr2 = D[expr, x, n] /. rule) // TraditionalForm
where FactorialPower is used and expr2 equivalent to
TraditionalForm[
expr3 = ReplacePart[expr2, 1 -> FunctionExpand[expr2[[1]]]] /.
Gamma[z_] :> (z - 1)!]
answered 7 hours ago
Bob HanlonBob Hanlon
66.2k3 gold badges37 silver badges102 bronze badges
$endgroup$
add a comment
|
$begingroup$
Clear["Global`*"]
rule = D[Sum[expr_, k_Symbol, kmin_, kmax_], x_, n_] :>
Sum[D[expr, x, n], k, kmin, kmax];
Format[γ[j_]] := Subscript[γ, j]
expr = Sum[γ[j] x^j, j, 0, n];
(expr2 = D[expr, x, n] /. rule) // TraditionalForm
where FactorialPower is used and expr2 equivalent to
TraditionalForm[
expr3 = ReplacePart[expr2, 1 -> FunctionExpand[expr2[[1]]]] /.
Gamma[z_] :> (z - 1)!]
answered 7 hours ago
Bob HanlonBob Hanlon
66.2k3 gold badges37 silver badges102 bronze badges
$endgroup$
Clear["Global`*"]
rule = D[Sum[expr_, k_Symbol, kmin_, kmax_], x_, n_] :>
Sum[D[expr, x, n], k, kmin, kmax];
Format[γ[j_]] := Subscript[γ, j]
expr = Sum[γ[j] x^j, j, 0, n];
(expr2 = D[expr, x, n] /. rule) // TraditionalForm
where FactorialPower is used and expr2 equivalent to
TraditionalForm[
expr3 = ReplacePart[expr2, 1 -> FunctionExpand[expr2[[1]]]] /.
Gamma[z_] :> (z - 1)!]
answered 7 hours ago
Bob HanlonBob Hanlon
66.2k3 gold badges37 silver badges102 bronze badges
answered 7 hours ago
Bob HanlonBob Hanlon
66.2k3 gold badges37 silver badges102 bronze badges
answered 7 hours ago
Bob HanlonBob Hanlon
66.2k3 gold badges37 silver badges102 bronze badges
answered 7 hours ago
Bob HanlonBob Hanlon
66.2k3 gold badges37 silver badges102 bronze badges
66.2k3 gold badges37 silver badges102 bronze badges
add a comment
|
add a comment
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the.polo is a new contributor. Be nice, and check out our Code of Conduct.
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the.polo is a new contributor. Be nice, and check out our Code of Conduct.
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