Under what condition can we analytically continue an equation?
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Suppose we have an equation
$$(partial_x^2+bpartial_x+h(x))f(x)=g(x)$$
which we known is satisfied for real $x$.
Under what conditions, can we continue it to
$$(partial_z^2+bpartial_z+h(z))f(z)=g(z)$$
for complex $z$?
complex-analysis
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up vote
2
down vote
favorite
Suppose we have an equation
$$(partial_x^2+bpartial_x+h(x))f(x)=g(x)$$
which we known is satisfied for real $x$.
Under what conditions, can we continue it to
$$(partial_z^2+bpartial_z+h(z))f(z)=g(z)$$
for complex $z$?
complex-analysis
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Suppose we have an equation
$$(partial_x^2+bpartial_x+h(x))f(x)=g(x)$$
which we known is satisfied for real $x$.
Under what conditions, can we continue it to
$$(partial_z^2+bpartial_z+h(z))f(z)=g(z)$$
for complex $z$?
complex-analysis
Suppose we have an equation
$$(partial_x^2+bpartial_x+h(x))f(x)=g(x)$$
which we known is satisfied for real $x$.
Under what conditions, can we continue it to
$$(partial_z^2+bpartial_z+h(z))f(z)=g(z)$$
for complex $z$?
complex-analysis
asked Aug 22 at 9:34
Wein Eld
207111
207111
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add a comment |Â
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