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This book consists of a selection of problems, each with a solution worked out in detail, dealing with the properties and applications of the Gamma function Gamma Function: [In Mathematics, the Gamma Function (Represented by the capital Gamma function is also called Eulerian integral of the second kind. Example (duplication formula). Prove that Γ(n)Γ(n + 1/2) = 21−2n. √ π Γ(2n). Solution. By the definition of beta function, we have. B(n,n) = 2. Factorial, Gamma and Beta Functions. Reading. Problems. Outline where the solution to I is obtained from Schaum's Handbook of Mathematical Functions.Using Gamma Function to Evaluate Integrals. Example(1). Evaluate: I = 0 ∞ x. 6 e. -2x dx. Solution: Letting y = 2x, we get. I = (1/128) 0 ∞. This is known as the geometric series formula, and is used in a variety of problems. we use the first definition its that strange sum of all the powers of 2.