Definite integraton f(x) / sqrt (-x^2-bx-c)

  • Thread starter ianbell
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Main Question or Discussion Point

I am interested in the definite integration of
f(x) / sqrt(-Q(x))
over the range of x for which quadratic
Q(x) = x^2 + b x + c is negative .

f(x) = sin(a x)/x in particular but others too.

Can anybody point me at any known formulae?

TIA.
 

Answers and Replies

1,222
2
This is a case for contour integration!
 
20
0
Can you elaborate?

Going complex, we might consider the imaginary part of
exp ( i a z) / ( z sqrt(-(z-q1)(z-q2) )
or more generally f(z) / sqrt(-(z-q1)(z-q2))
as z moves along the real axis from q1 to q2 , the two real roots of quadratic Q(x)=x^2+bx+c.
 

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