Final answer:
The gamma function for Γ(6) equals 5!, which calculates to 120. The value of Γ(5/2) requires using the gamma function's properties and is not straightforward, while further clarification is needed for the expression 1(4,2).
Step-by-step explanation:
The gamma function, denoted as Γ(x), is a function that extends the factorial function to real and complex numbers. It is defined for positive real numbers and by analytic continuation, for complex numbers with a non-negative real part, except for the non-positive integers. For positive integer values, the gamma function is equal to the factorial of the number decremented by one, meaning Γ(n) = (n - 1)!. Therefore, the solutions to the given problems are:
- (a) Γ(6) = 5!
- (b) The Gamma function is not explicitly defined for I(5/2), possibly the student meant Γ(5/2). If that is the case, Γ(5/2) is not as straightforward and is equal to (3/2)! which can be calculated using the gamma function's properties.
- (c) There is a lack of clarity regarding 1(4,2). The notation does not match known properties of the gamma function, so additional clarification would be required to provide an answer.
For Γ(6), using the properties of the gamma function:
Γ(6) = (6 - 1)! = 5! = 5 × 4 × 3 × 2 × 1 = 120