How to obtain the explicit solution of the following integral equation
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I'm considering the following integral equation
$$
f(x,y,z)=x+int_0^xint_0^yint_0^z f(u,v,w) dudvdw
$$
It seems that
$$
f(x,y,z)=sum_ngeq 0fracx^n+1 y^n z^n(n+1)!n!n!
$$
is the solution. How to transform it into a closed form instead of a series?
calculus differential-equations power-series integral-equations
add a comment |Â
up vote
2
down vote
favorite
I'm considering the following integral equation
$$
f(x,y,z)=x+int_0^xint_0^yint_0^z f(u,v,w) dudvdw
$$
It seems that
$$
f(x,y,z)=sum_ngeq 0fracx^n+1 y^n z^n(n+1)!n!n!
$$
is the solution. How to transform it into a closed form instead of a series?
calculus differential-equations power-series integral-equations
$partial f / partial x$ is a function of $xyz$, and I wonder what is the "closed form" of it you expect to find (in the two-variable case it would be $I_0(sqrt2xy)$).
â metamorphy
Aug 12 at 14:28
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I'm considering the following integral equation
$$
f(x,y,z)=x+int_0^xint_0^yint_0^z f(u,v,w) dudvdw
$$
It seems that
$$
f(x,y,z)=sum_ngeq 0fracx^n+1 y^n z^n(n+1)!n!n!
$$
is the solution. How to transform it into a closed form instead of a series?
calculus differential-equations power-series integral-equations
I'm considering the following integral equation
$$
f(x,y,z)=x+int_0^xint_0^yint_0^z f(u,v,w) dudvdw
$$
It seems that
$$
f(x,y,z)=sum_ngeq 0fracx^n+1 y^n z^n(n+1)!n!n!
$$
is the solution. How to transform it into a closed form instead of a series?
calculus differential-equations power-series integral-equations
edited Aug 12 at 8:02
user529760
asked Aug 12 at 6:50
Yuhang
780118
780118
$partial f / partial x$ is a function of $xyz$, and I wonder what is the "closed form" of it you expect to find (in the two-variable case it would be $I_0(sqrt2xy)$).
â metamorphy
Aug 12 at 14:28
add a comment |Â
$partial f / partial x$ is a function of $xyz$, and I wonder what is the "closed form" of it you expect to find (in the two-variable case it would be $I_0(sqrt2xy)$).
â metamorphy
Aug 12 at 14:28
$partial f / partial x$ is a function of $xyz$, and I wonder what is the "closed form" of it you expect to find (in the two-variable case it would be $I_0(sqrt2xy)$).
â metamorphy
Aug 12 at 14:28
$partial f / partial x$ is a function of $xyz$, and I wonder what is the "closed form" of it you expect to find (in the two-variable case it would be $I_0(sqrt2xy)$).
â metamorphy
Aug 12 at 14:28
add a comment |Â
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$partial f / partial x$ is a function of $xyz$, and I wonder what is the "closed form" of it you expect to find (in the two-variable case it would be $I_0(sqrt2xy)$).
â metamorphy
Aug 12 at 14:28