Expressing the solution of $intfrac{x^2 dx}{a-sqrt{b^2+x^2}-sqrt{c^2+x^2}}$ without the use of elliptic...
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Mathematica is able to provide me with an analytic solution to this integral, but it involves EllipticF's, EllipticE's, and EllipticPi's, all of complex variables. Are there any integral tables that provide a solution without the use of incomplete elliptic integrals of complex arguments?
integration elliptic-integrals
asked Jan 11 at 22:05
DannyDanny
333
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add a comment |
$begingroup$
Mathematica is able to provide me with an analytic solution to this integral, but it involves EllipticF's, EllipticE's, and EllipticPi's, all of complex variables. Are there any integral tables that provide a solution without the use of incomplete elliptic integrals of complex arguments?
integration elliptic-integrals
asked Jan 11 at 22:05
DannyDanny
333
$endgroup$
3
$begingroup$
I doubt a closed form not involving elliptic integrals even exists. There's a reason we have defined those special functions the way we have
$endgroup$
– clathratus
Jan 11 at 23:03
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I don’t wish to avoid elliptic integrals, only elliptic integrals with complex arguments. I know the solution should be real for real x, but Mathematica will only express the solution with complex arguments.
$endgroup$
– Danny
Jan 13 at 23:23
add a comment |
$begingroup$
Mathematica is able to provide me with an analytic solution to this integral, but it involves EllipticF's, EllipticE's, and EllipticPi's, all of complex variables. Are there any integral tables that provide a solution without the use of incomplete elliptic integrals of complex arguments?
integration elliptic-integrals
asked Jan 11 at 22:05
DannyDanny
333
$endgroup$
Mathematica is able to provide me with an analytic solution to this integral, but it involves EllipticF's, EllipticE's, and EllipticPi's, all of complex variables. Are there any integral tables that provide a solution without the use of incomplete elliptic integrals of complex arguments?
integration elliptic-integrals
integration elliptic-integrals
asked Jan 11 at 22:05
DannyDanny
333
asked Jan 11 at 22:05
DannyDanny
333
asked Jan 11 at 22:05
DannyDanny
333
asked Jan 11 at 22:05
DannyDanny
333
asked Jan 11 at 22:05
DannyDanny
333
333
3
$begingroup$
I doubt a closed form not involving elliptic integrals even exists. There's a reason we have defined those special functions the way we have
$endgroup$
– clathratus
Jan 11 at 23:03
$begingroup$
I don’t wish to avoid elliptic integrals, only elliptic integrals with complex arguments. I know the solution should be real for real x, but Mathematica will only express the solution with complex arguments.
$endgroup$
– Danny
Jan 13 at 23:23
add a comment |
3
$begingroup$
I doubt a closed form not involving elliptic integrals even exists. There's a reason we have defined those special functions the way we have
$endgroup$
– clathratus
Jan 11 at 23:03
$begingroup$
I don’t wish to avoid elliptic integrals, only elliptic integrals with complex arguments. I know the solution should be real for real x, but Mathematica will only express the solution with complex arguments.
$endgroup$
– Danny
Jan 13 at 23:23
3
3
$begingroup$
I doubt a closed form not involving elliptic integrals even exists. There's a reason we have defined those special functions the way we have
$endgroup$
– clathratus
Jan 11 at 23:03
$begingroup$
I doubt a closed form not involving elliptic integrals even exists. There's a reason we have defined those special functions the way we have
$endgroup$
– clathratus
Jan 11 at 23:03
$begingroup$
I don’t wish to avoid elliptic integrals, only elliptic integrals with complex arguments. I know the solution should be real for real x, but Mathematica will only express the solution with complex arguments.
$endgroup$
– Danny
Jan 13 at 23:23
$begingroup$
I don’t wish to avoid elliptic integrals, only elliptic integrals with complex arguments. I know the solution should be real for real x, but Mathematica will only express the solution with complex arguments.
$endgroup$
– Danny
Jan 13 at 23:23
add a comment |
0
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$begingroup$
I doubt a closed form not involving elliptic integrals even exists. There's a reason we have defined those special functions the way we have
$endgroup$
– clathratus
Jan 11 at 23:03
$begingroup$
I don’t wish to avoid elliptic integrals, only elliptic integrals with complex arguments. I know the solution should be real for real x, but Mathematica will only express the solution with complex arguments.
$endgroup$
– Danny
Jan 13 at 23:23