Notation for Higher Antiderivatives?












6












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    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.
    $endgroup$
    – Ian
    Dec 26 '18 at 18:21










  • $begingroup$
    @Ian he said antiderivatives not integrals.
    $endgroup$
    – Ben W
    Dec 26 '18 at 18:22






  • 1




    $begingroup$
    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.
    $endgroup$
    – Ben W
    Dec 26 '18 at 18:26










  • $begingroup$
    @BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
    $endgroup$
    – Arthur
    Dec 26 '18 at 19:20








  • 1




    $begingroup$
    You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
    $endgroup$
    – J.G.
    Dec 26 '18 at 19:35
















6












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    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.
    $endgroup$
    – Ian
    Dec 26 '18 at 18:21










  • $begingroup$
    @Ian he said antiderivatives not integrals.
    $endgroup$
    – Ben W
    Dec 26 '18 at 18:22






  • 1




    $begingroup$
    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.
    $endgroup$
    – Ben W
    Dec 26 '18 at 18:26










  • $begingroup$
    @BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
    $endgroup$
    – Arthur
    Dec 26 '18 at 19:20








  • 1




    $begingroup$
    You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
    $endgroup$
    – J.G.
    Dec 26 '18 at 19:35














6












6








6





$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 26 '18 at 19:40







Mohammad Riazi-Kermani

















asked Dec 26 '18 at 18:19









Mohammad Riazi-KermaniMohammad Riazi-Kermani

41.6k42061




41.6k42061








  • 1




    $begingroup$
    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.
    $endgroup$
    – Ian
    Dec 26 '18 at 18:21










  • $begingroup$
    @Ian he said antiderivatives not integrals.
    $endgroup$
    – Ben W
    Dec 26 '18 at 18:22






  • 1




    $begingroup$
    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.
    $endgroup$
    – Ben W
    Dec 26 '18 at 18:26










  • $begingroup$
    @BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
    $endgroup$
    – Arthur
    Dec 26 '18 at 19:20








  • 1




    $begingroup$
    You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
    $endgroup$
    – J.G.
    Dec 26 '18 at 19:35














  • 1




    $begingroup$
    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.
    $endgroup$
    – Ian
    Dec 26 '18 at 18:21










  • $begingroup$
    @Ian he said antiderivatives not integrals.
    $endgroup$
    – Ben W
    Dec 26 '18 at 18:22






  • 1




    $begingroup$
    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.
    $endgroup$
    – Ben W
    Dec 26 '18 at 18:26










  • $begingroup$
    @BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
    $endgroup$
    – Arthur
    Dec 26 '18 at 19:20








  • 1




    $begingroup$
    You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
    $endgroup$
    – J.G.
    Dec 26 '18 at 19:35








1




1




$begingroup$
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.
$endgroup$
– Ian
Dec 26 '18 at 18:21




$begingroup$
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.
$endgroup$
– Ian
Dec 26 '18 at 18:21












$begingroup$
@Ian he said antiderivatives not integrals.
$endgroup$
– Ben W
Dec 26 '18 at 18:22




$begingroup$
@Ian he said antiderivatives not integrals.
$endgroup$
– Ben W
Dec 26 '18 at 18:22




1




1




$begingroup$
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.
$endgroup$
– Ben W
Dec 26 '18 at 18:26




$begingroup$
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.
$endgroup$
– Ben W
Dec 26 '18 at 18:26












$begingroup$
@BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
$endgroup$
– Arthur
Dec 26 '18 at 19:20






$begingroup$
@BenW Your last example becomes prettier if you still use the multiple integrals command: $iintcdotsint$ versus $intintcdotsint$.
$endgroup$
– Arthur
Dec 26 '18 at 19:20






1




1




$begingroup$
You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
$endgroup$
– J.G.
Dec 26 '18 at 19:35




$begingroup$
You may like one of the conventions in en.wikipedia.org/wiki/Fractional_calculus#Fractional_integrals
$endgroup$
– J.G.
Dec 26 '18 at 19:35










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."






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    1






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    oldest

    votes






    active

    oldest

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    2












    $begingroup$

    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."






    share|cite|improve this answer











    $endgroup$


















      2












      $begingroup$

      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."






      share|cite|improve this answer











      $endgroup$
















        2












        2








        2





        $begingroup$

        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."






        share|cite|improve this answer











        $endgroup$



        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."







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Dec 26 '18 at 19:24

























        answered Dec 26 '18 at 19:15









        TheSimpliFireTheSimpliFire

        12.7k62461




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