Is there a difference between $g(x,y)$ and $g(x;y)$?












1














Is there a reason that the second notation uses a semicolon?



Here's the definition:




we say $g(x;y)$ is a Green's function



$$g(x;y) = left{
begin{array}{lr}
sin(kx)sin(k(y-1)/ksin(k) & : x lt y\
sin(ky)sin(k(x-1)/ksin(k) & : y lt x\ end{array}
right.$$







notation







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  • 6




    There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x; y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.
    – littleO
    Jan 4 at 14:03








  • 1




    @littleO it seems like you could make that comment verbatim into an answer
    – Mark S.
    Jan 4 at 14:15
















1














Is there a reason that the second notation uses a semicolon?



Here's the definition:




we say $g(x;y)$ is a Green's function



$$g(x;y) = left{
begin{array}{lr}
sin(kx)sin(k(y-1)/ksin(k) & : x lt y\
sin(ky)sin(k(x-1)/ksin(k) & : y lt x\ end{array}
right.$$







notation







share|cite|improve this question




















  • 6




    There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x; y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.
    – littleO
    Jan 4 at 14:03








  • 1




    @littleO it seems like you could make that comment verbatim into an answer
    – Mark S.
    Jan 4 at 14:15














1












1








1







Is there a reason that the second notation uses a semicolon?



Here's the definition:




we say $g(x;y)$ is a Green's function



$$g(x;y) = left{
begin{array}{lr}
sin(kx)sin(k(y-1)/ksin(k) & : x lt y\
sin(ky)sin(k(x-1)/ksin(k) & : y lt x\ end{array}
right.$$







notation







share|cite|improve this question















Is there a reason that the second notation uses a semicolon?



Here's the definition:




we say $g(x;y)$ is a Green's function



$$g(x;y) = left{
begin{array}{lr}
sin(kx)sin(k(y-1)/ksin(k) & : x lt y\
sin(ky)sin(k(x-1)/ksin(k) & : y lt x\ end{array}
right.$$







notation




notation






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share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 4 at 14:48









Le Anh Dung

1,0531521




1,0531521










asked Jan 4 at 13:59









user29418user29418

444513




444513








  • 6




    There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x; y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.
    – littleO
    Jan 4 at 14:03








  • 1




    @littleO it seems like you could make that comment verbatim into an answer
    – Mark S.
    Jan 4 at 14:15














  • 6




    There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x; y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.
    – littleO
    Jan 4 at 14:03








  • 1




    @littleO it seems like you could make that comment verbatim into an answer
    – Mark S.
    Jan 4 at 14:15








6




6




There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x; y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.
– littleO
Jan 4 at 14:03






There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x; y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.
– littleO
Jan 4 at 14:03






1




1




@littleO it seems like you could make that comment verbatim into an answer
– Mark S.
Jan 4 at 14:15




@littleO it seems like you could make that comment verbatim into an answer
– Mark S.
Jan 4 at 14:15










1 Answer
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I'll post my comment here so that the question receives an answer:



There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x;y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.






share|cite|improve this answer





















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    1 Answer
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    I'll post my comment here so that the question receives an answer:



    There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x;y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.






    share|cite|improve this answer


























      3














      I'll post my comment here so that the question receives an answer:



      There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x;y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.






      share|cite|improve this answer
























        3












        3








        3






        I'll post my comment here so that the question receives an answer:



        There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x;y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.






        share|cite|improve this answer












        I'll post my comment here so that the question receives an answer:



        There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x mapsto g(x;y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 4 at 14:23









        littleOlittleO

        29.3k644109




        29.3k644109






























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