(a) Define Gamma function and prove that $\Gamma\left(\frac{1}{2}\rig…

Question

(a) Define Gamma function and prove that $\Gamma\left(\frac{1}{2}\right) = \sqrt{\pi}$.

(b) Prove that

$$\int_0^t \text{erf}_c(ax) \, dx = t \text{erf}_c(at) - \frac{1}{a\sqrt{\pi}}(e^{-a^2t^2} - 1)$$

(c) Evaluate $\iiint \cos(x+y+z) \, dxdydz$ over the region of the positive octant cut off by the plane $x + y + z = \pi$.

Related pages

• Gamma Function — topic
• Engineering Mathematics-I syllabus

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