Notation for Higher Antiderivatives?
Higher derivative are blessed with many notations.
For example $$ f',f'',...$$ or $$ frac {dy}{dx}, frac {d^2 y}{dx^2},...$$
I have not seen any notations for higher anti-derivatives.
For example, the higher anti-derivatives of $$f(x)=2x+5$$ are $$x^2+5x+c_1, frac {x^3}{3} +frac {5}{2} x^2 + c_1x +c_2,.....$$
Are there notations for higher anti-derivatives?
integration
asked Dec 26 '18 at 18:19
Mohammad Riazi-Kermani
40.8k42059
|
show 1 more comment
Higher derivative are blessed with many notations.
For example $$ f',f'',...$$ or $$ frac {dy}{dx}, frac {d^2 y}{dx^2},...$$
I have not seen any notations for higher anti-derivatives.
For example, the higher anti-derivatives of $$f(x)=2x+5$$ are $$x^2+5x+c_1, frac {x^3}{3} +frac {5}{2} x^2 + c_1x +c_2,.....$$
Are there notations for higher anti-derivatives?
integration
asked Dec 26 '18 at 18:19
Mohammad Riazi-Kermani
40.8k42059
1
I find usually if this is coming up, the boundary conditions are somehow built into the problem, so notations like $int_0^x int_0^{x'} f(x'') dx'' dx'$ become suitable.
– Ian
Dec 26 '18 at 18:21
@Ian he said antiderivatives not integrals.
– Ben W
Dec 26 '18 at 18:22
1
Interesting question. For the first few antiderivatives we just repeat the $int$ symbol. In fact, latex allows us to write conveniently up to four of them using the iiiint command, like so: $iiiint$. At a certain point, of course, this becomes impractical. You could write it this way: $underbrace{intintcdotsint}_{ntext{ times}}$. But I wonder if there is something more compact.
– Ben W
Dec 26 '18 at 18:26
@BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
– Arthur
Dec 26 '18 at 19:20
1
You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
– J.G.
Dec 26 '18 at 19:35
|
show 1 more comment
Higher derivative are blessed with many notations.
For example $$ f',f'',...$$ or $$ frac {dy}{dx}, frac {d^2 y}{dx^2},...$$
I have not seen any notations for higher anti-derivatives.
For example, the higher anti-derivatives of $$f(x)=2x+5$$ are $$x^2+5x+c_1, frac {x^3}{3} +frac {5}{2} x^2 + c_1x +c_2,.....$$
Are there notations for higher anti-derivatives?
integration
asked Dec 26 '18 at 18:19
Mohammad Riazi-Kermani
40.8k42059
Higher derivative are blessed with many notations.
For example $$ f',f'',...$$ or $$ frac {dy}{dx}, frac {d^2 y}{dx^2},...$$
I have not seen any notations for higher anti-derivatives.
For example, the higher anti-derivatives of $$f(x)=2x+5$$ are $$x^2+5x+c_1, frac {x^3}{3} +frac {5}{2} x^2 + c_1x +c_2,.....$$
Are there notations for higher anti-derivatives?
integration
integration
asked Dec 26 '18 at 18:19
Mohammad Riazi-Kermani
40.8k42059
asked Dec 26 '18 at 18:19
Mohammad Riazi-Kermani
40.8k42059
edited Dec 26 '18 at 19:40
asked Dec 26 '18 at 18:19
Mohammad Riazi-Kermani
40.8k42059
asked Dec 26 '18 at 18:19
Mohammad Riazi-Kermani
40.8k42059
asked Dec 26 '18 at 18:19
Mohammad Riazi-Kermani
40.8k42059
40.8k42059
1
I find usually if this is coming up, the boundary conditions are somehow built into the problem, so notations like $int_0^x int_0^{x'} f(x'') dx'' dx'$ become suitable.
– Ian
Dec 26 '18 at 18:21
@Ian he said antiderivatives not integrals.
– Ben W
Dec 26 '18 at 18:22
1
Interesting question. For the first few antiderivatives we just repeat the $int$ symbol. In fact, latex allows us to write conveniently up to four of them using the iiiint command, like so: $iiiint$. At a certain point, of course, this becomes impractical. You could write it this way: $underbrace{intintcdotsint}_{ntext{ times}}$. But I wonder if there is something more compact.
– Ben W
Dec 26 '18 at 18:26
@BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
– Arthur
Dec 26 '18 at 19:20
1
You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
– J.G.
Dec 26 '18 at 19:35
|
show 1 more comment
1
I find usually if this is coming up, the boundary conditions are somehow built into the problem, so notations like $int_0^x int_0^{x'} f(x'') dx'' dx'$ become suitable.
– Ian
Dec 26 '18 at 18:21
@Ian he said antiderivatives not integrals.
– Ben W
Dec 26 '18 at 18:22
1
Interesting question. For the first few antiderivatives we just repeat the $int$ symbol. In fact, latex allows us to write conveniently up to four of them using the iiiint command, like so: $iiiint$. At a certain point, of course, this becomes impractical. You could write it this way: $underbrace{intintcdotsint}_{ntext{ times}}$. But I wonder if there is something more compact.
– Ben W
Dec 26 '18 at 18:26
@BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
– Arthur
Dec 26 '18 at 19:20
1
You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
– J.G.
Dec 26 '18 at 19:35
1
1
I find usually if this is coming up, the boundary conditions are somehow built into the problem, so notations like $int_0^x int_0^{x'} f(x'') dx'' dx'$ become suitable.
– Ian
Dec 26 '18 at 18:21
I find usually if this is coming up, the boundary conditions are somehow built into the problem, so notations like $int_0^x int_0^{x'} f(x'') dx'' dx'$ become suitable.
– Ian
Dec 26 '18 at 18:21
@Ian he said antiderivatives not integrals.
– Ben W
Dec 26 '18 at 18:22
@Ian he said antiderivatives not integrals.
– Ben W
Dec 26 '18 at 18:22
1
1
Interesting question. For the first few antiderivatives we just repeat the $int$ symbol. In fact, latex allows us to write conveniently up to four of them using the iiiint command, like so: $iiiint$. At a certain point, of course, this becomes impractical. You could write it this way: $underbrace{intintcdotsint}_{ntext{ times}}$. But I wonder if there is something more compact.
– Ben W
Dec 26 '18 at 18:26
Interesting question. For the first few antiderivatives we just repeat the $int$ symbol. In fact, latex allows us to write conveniently up to four of them using the iiiint command, like so: $iiiint$. At a certain point, of course, this becomes impractical. You could write it this way: $underbrace{intintcdotsint}_{ntext{ times}}$. But I wonder if there is something more compact.
– Ben W
Dec 26 '18 at 18:26
@BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
– Arthur
Dec 26 '18 at 19:20
@BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
– Arthur
Dec 26 '18 at 19:20
1
1
You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
– J.G.
Dec 26 '18 at 19:35
You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
– J.G.
Dec 26 '18 at 19:35
|
show 1 more comment
1 Answer
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Using Lagrange's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=f^{(-n)}(x)$$ Using Newton's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=overset{n}{overset{'}{y}}$$ although it "did not become widespread because of printing difficulties."
answered Dec 26 '18 at 19:15
TheSimpliFire
12.3k62259
add a comment |
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Using Lagrange's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=f^{(-n)}(x)$$ Using Newton's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=overset{n}{overset{'}{y}}$$ although it "did not become widespread because of printing difficulties."
answered Dec 26 '18 at 19:15
TheSimpliFire
12.3k62259
add a comment |
Using Lagrange's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=f^{(-n)}(x)$$ Using Newton's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=overset{n}{overset{'}{y}}$$ although it "did not become widespread because of printing difficulties."
answered Dec 26 '18 at 19:15
TheSimpliFire
12.3k62259
add a comment |
Using Lagrange's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=f^{(-n)}(x)$$ Using Newton's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=overset{n}{overset{'}{y}}$$ although it "did not become widespread because of printing difficulties."
answered Dec 26 '18 at 19:15
TheSimpliFire
12.3k62259
Using Lagrange's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=f^{(-n)}(x)$$ Using Newton's notation as detailed in the link, $$underbrace{iintcdotsint}_{ntext{ times}}=overset{n}{overset{'}{y}}$$ although it "did not become widespread because of printing difficulties."
answered Dec 26 '18 at 19:15
TheSimpliFire
12.3k62259
edited Dec 26 '18 at 19:24
answered Dec 26 '18 at 19:15
TheSimpliFire
12.3k62259
answered Dec 26 '18 at 19:15
TheSimpliFire
12.3k62259
answered Dec 26 '18 at 19:15
TheSimpliFire
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12.3k62259
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I find usually if this is coming up, the boundary conditions are somehow built into the problem, so notations like $int_0^x int_0^{x'} f(x'') dx'' dx'$ become suitable.
– Ian
Dec 26 '18 at 18:21
@Ian he said antiderivatives not integrals.
– Ben W
Dec 26 '18 at 18:22
1
Interesting question. For the first few antiderivatives we just repeat the $int$ symbol. In fact, latex allows us to write conveniently up to four of them using the iiiint command, like so: $iiiint$. At a certain point, of course, this becomes impractical. You could write it this way: $underbrace{intintcdotsint}_{ntext{ times}}$. But I wonder if there is something more compact.
– Ben W
Dec 26 '18 at 18:26
@BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
– Arthur
Dec 26 '18 at 19:20
1
You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
– J.G.
Dec 26 '18 at 19:35