Question

1. Gamma function of n (n>0), is defined as​

Answer 1

Answer: Hey mate  

Step-by-step explanation:

For a positive whole number n, the factorial (written as n!) is defined by n! = 1 × 2 × 3 ×⋯× (n − 1) × n. For example, 5! = 1 × 2 × 3 × 4 × 5 = 120. But this formula is meaningless if n is not an integer.

To extend the factorial to any real number x > 0 (whether or not x is a whole number), the gamma function is defined as

Γ(x) = Integral on the interval [0, ∞] of∫ 0∞t x −1 e−t dt.

Answer 2

SOLUTION

TO DEFINE

The Gamma function

EVALUATION

The Gamma function is denoted by Γ(n) and defined as :

$\displaystyle \Gamma \: (n) = \int\limits_{- \infty}^{\infty} e^{-x} \: {x}^{n - 1} \, dx \: \: \:$

Which converges for n > 0

Useful properties of Gamma function :

$1. \: \Gamma (n + 1) =n \: \Gamma (n)$

$2. \: \: \Gamma (1) = 1$

$3. \: \: \Gamma (n + 1) = n \: !$

provided n is a positive integer

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