# How to assume that a function is positive for all arguments?

Posted 10 years ago
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 When I calculate an integral of the form:Integrate[1/((f(a)+I*x)*(f(b)+I*x)),{x,-Infinity, Infinity}],where I is the imaginary unit. How can I assume that f(a) is a positive function for all values of its argument? I am not interested in changing the function to a constant and then assuming the constants are >0 since the real problem is complicated and I need to keep f(a) a function.
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Posted 10 years ago
 In[1]:= Integrate[1/((f[a] + I*x)*(f[b] + I*x)), {x, -Infinity, Infinity}, Assumptions -> {f[a]>0, f[b]>0}]Out[1]= 0
Posted 10 years ago
 The point is that in the general problem I do not know a priori all the arguments of the function and it is not practical to enumerate them. I wrote this integral as an example. I asked if there is a way to tell Mathematica to consider the function f[_]>0 (for any argument)? Maybe it is a little pathological to consider the integral which is 0 so one might as an example consider instead:Integrate[1/((f(a) + I*x)*(f(b) - I*x)), {x, -Infinity, Infinity}]
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