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:
“The foregoing generations beheld God and nature face to face; we, through their eyes. Why should not we also enjoy an original relation to the universe? Why should not we have a poetry and philosophy of insight and not of tradition, and a religion by revelation to us, and not the history of theirs?”
—Ralph Waldo Emerson (1803–1882)
“... a worker was seldom so much annoyed by what he got as by what he got in relation to his fellow workers.”
—Mary Barnett Gilson (1877–?)
“Whoever has a keen eye for profits, is blind in relation to his craft.”
—Sophocles (497–406/5 B.C.)
“... the function of art is to do more than tell it like it is—it’s to imagine what is possible.”
—bell hooks (b. c. 1955)