Some Gaussian Integrals
Some Gaussian Integrals
The well-known Gaussian integral dx= can be evaluated in closed form, even though there is no elementary function equal to the indefinite integral . More generally, integrals of the form dx can be evaluated for positive integers [1]. In this Demonstration, we perform numerical integrations for dx, with and . The results are then represented as areas under a curve (shown in red).
∞
∫
0
-
2
x
e
π
2
∫dx
-
2
x
e
∞
∫
0
n
x
-b
2
x
e
n
p
∫
0
n
x
-b
2
x
e
n=0,1,2,3
b=1,2,…,5
References
References
[1] E. W. Weisstein, "Gaussian Integral," Wolfram MathWorld. (Jan 25, 2016) mathworld.wolfram.com/GaussianIntegral.html.
External Links
External Links
Permanent Citation
Permanent Citation
Casimir Kothari
"Some Gaussian Integrals"
http://demonstrations.wolfram.com/SomeGaussianIntegrals/
Wolfram Demonstrations Project
Published: January 26, 2016