Chapter 11.5, Problem 2P

Without computer or tables, but just using facts you know, sketch a quick rough graph of the $\Gamma$ function from -2 to $3 .$ Hint: This is easy; don’t make a big job of it. From Section $3,$ you know the values of the $\Gamma$ function at the positive integers in terms of factorials. From Problem $1,$ you can easily find and plot the $\Gamma$ function at $\pm 1/2,\pm 3/2.$ (Approximate $\sqrt{\pi }$ as a little less than 2 .) From ( 4.1 ) and the discussion following it, you know that the $\Gamma$ function tends to plus or minus infinity at 0 and the negative integers, and you know the intervals where it is positive or negative. After sketching your graph, make a computer plot of the $\Gamma$ function from -5 to 5 and compare your sketch.