This article generalizes the famous Wallis’s formula
for k ≥ 0 , to an integral over the unit sphere S
n-1. An application to the integral of polynomials over S
n-1 is discussed.
Willis Formula Unit SphereCite this paper
Namazi, J. (2018) A Generalized Wallis Formula. Applied Mathematics, 9, 207-209. https://doi.org/10.4236/am.2018.93015
ReferencesMuller, C. (1966) Spherical Harmonics. Springer-Verlag Berlin Heidelberg.
https://doi.org/10.1007/BFb0094775Macrobert, T.M. (1948) Spherical Harmonics: An Elementary Treatise on Harmonic Functions with Applications. Dover Publications, New York.Stein, E. and Weiss, G. (1971) Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton.Jeffrey, H. and Jeffrey, B. (1999) Methods of Mathematical Physics. 3rd Edition, Cambridge University Press, Cambridge.
for k ≥ 0 , to an integral over the unit sphere S
n-1. An application to the integral of polynomials over S
n-1 is discussed.