Other important functional equations for the gamma function are Euler 's reflection formula which implies and the duplication formula The duplication formula is a special case of the multiplication theorem A simple but useful property , which can be seen from the limit definition , is : Perhaps the best-known value of the gamma function at a non-integer argument is which can be found by setting z = 1\/2 in the reflection or duplication formulas , by using the relation to the beta function given below with x = y = 1\/2 , or simply by making the substitution u = √ t in the integral definition of the gamma function , resulting in a Gaussian integral .
It says : This means The gamma function also has a duplication formula : This formula is a special case of the multiplication theorem A property of the function is that : A famous value of the function at a non-integral point is : This is found if we set z = 1\/2 in the reflection or duplication formulas .