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Math Help - Need a Laplace inversion formula

  1. #1
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    Need a Laplace inversion formula

    Is there any Laplace inversion formula for any of these equations

    f(s)=\frac{1}{a\sqrt{s+b}+c\sqrt{s/d+b}}
    or
     <br />
f(s)=\frac{\exp{(-k\sqrt{s+b})}}{a\sqrt{s+b}+c\sqrt{s/d+b}}<br />

    the inversion is easy if d=1, but I want to find the general form. Thank you.
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  2. #2
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    Quote Originally Posted by Ehsan View Post
    Is there any Laplace inversion formula for any of these equations

    f(s)=\frac{1}{a\sqrt{s+b}+c\sqrt{s/d+b}}
    or
     <br />
f(s)=\frac{\exp{(-k\sqrt{s+b})}}{a\sqrt{s+b}+c\sqrt{s/d+b}}<br />

    the inversion is easy if d=1, but I want to find the general form. Thank you.
    Well if you take the factor of 1/d out of the square root then you get a form that is equivalent to if d = 1. So if that form is easy for you, there you go.
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  3. #3
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    I cannot invert it taking the factor of 1/d out

    if d=1 then the square roots become identical (which makes it easy to invert) but if I take the factor 1/d out of the square root the equations become:

     <br />
f(s)=\frac{1}{a\sqrt{s+b}+\frac{c}{\sqrt{d}}\sqrt{  s+bd}}<br />
    or
     <br />
f(s)=\frac{\exp{(-k\sqrt{s+b})}}{a\sqrt{s+b}+\frac{c}{\sqrt{d}}\sqrt  {s+bd}}<br />

    which I cannot invert.
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  4. #4
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    Quote Originally Posted by Ehsan View Post
    if d=1 then the square roots become identical (which makes it easy to invert) but if I take the factor 1/d out of the square root the equations become:

     <br />
f(s)=\frac{1}{a\sqrt{s+b}+\frac{c}{\sqrt{d}}\sqrt{  s+bd}}<br />
    or
     <br />
f(s)=\frac{\exp{(-k\sqrt{s+b})}}{a\sqrt{s+b}+\frac{c}{\sqrt{d}}\sqrt  {s+bd}}<br />

    which I cannot invert.
    Whoops! Right you are. I'll have a think while I'm asleep (which is very soon).
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