Re: Can I solve these integrals?



Peltio wrote:
"JH" wrote


int( sin(x) / cos((B+x)/2) * exp(-(A*x)^2), x=0..PI)
int( sin(x) * cos((B+x)/2) * exp(-(A*x)^2), x=0..PI)

Mathematica seems be able to evaluate these integral (with hypergeom functions) but I hope it can be resolved exactly...


With 'exactly', you mean with rational functions only ?
Becuse, strictly speaking, the integrands themselves are not 'exact' since
they involve the 'special functions' sin and cos.

I mean with all functions whose are easily computed (cos, sin, erf, gamma, etc...). Actually, I'm searching for a formulation whose evaluation would be faster than a numerical computation of the integral.

Cheers

JH
.



Relevant Pages

  • Re: Can I solve these integrals?
    ... Becuse, strictly speaking, the integrands themselves are not 'exact' since ... they involve the 'special functions' sin and cos. ...
    (sci.math.symbolic)
  • Re: generate all possible math expr of one term
    ... The result lisp expression should match ... (+ X (TAN Y)) ... (+ X (COS Y)) ... (+ X (SIN Y)) ...
    (comp.lang.lisp)
  • Re: sin x / x tends to 1...
    ... that it's easy to show that the circumference of the unit circle ... >sin x, that we can call psin x, the limit is obvious. ... smallest positive zero of cos. ... I into the first quadrant, and that c is 1-1 on I. ...
    (sci.math)
  • Re: Mixed Coordinate conversion - ra from long and dec
    ... function of celestial longitude and declination. ... sin l cos b = cos e sin a cos d + sin e sin d ...
    (sci.astro.amateur)
  • Re: opponents of taylor and lhospital ?
    ... Suppose a high school senior taking the AP Calculus exam ... There are other ways to show that d/dx= cos x, ... computing the limit of (sin x)/x first. ... BUT practically all Calculus textbooks derive the limit of sin/x ...
    (sci.math)