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

Posted 11 years ago
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.
POSTED BY: Ivan Balog
2 Replies
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}]
POSTED BY: Ivan Balog
Posted 11 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 BY: Bill Simpson
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