Relation To The Gamma Function
The integrand is an even function,
Thus, after the change of variable, this turns into the Euler integral
where Γ is the gamma function. This shows why the factorial of a half-integer is a rational multiple of . More generally,
Read more about this topic: Gaussian Integral
Famous quotes containing the words relation to the, relation to, relation and/or function:
“Only in a house where one has learnt to be lonely does one have this solicitude for things. One’s relation to them, the daily seeing or touching, begins to become love, and to lay one open to pain.”
—Elizabeth Bowen (1899–1973)
“The whole point of Camp is to dethrone the serious. Camp is playful, anti-serious. More precisely, Camp involves a new, more complex relation to “the serious.” One can be serious about the frivolous, frivolous about the serious.”
—Susan Sontag (b. 1933)
“The adolescent does not develop her identity and individuality by moving outside her family. She is not triggered by some magic unconscious dynamic whereby she rejects her family in favour of her peers or of a larger society.... She continues to develop in relation to her parents. Her mother continues to have more influence over her than either her father or her friends.”
—Terri Apter (20th century)
“To make us feel small in the right way is a function of art; men can only make us feel small in the wrong way.”
—E.M. (Edward Morgan)