The integrals$\mathfrak{E}_p (x) = (p!)^{ - 1} \mathop \smallint \limits_0^\infty \varepsilon ^p (\varepsilon + x\varepsilon ^3 )^{ - 1} e^{ - \varepsilon } d\varepsilon$ and$\mathfrak{F}_p (x) = (p!)^{ - 1} \mathop \smallint \limits_0^\infty \varepsilon ^p (\varepsilon + x\varepsilon ^3 )^{ - 2} e^{ - \varepsilon } d\varepsilon$ and their tabulationand their tabulation

Summary

These integrals are fundamental to the theory of the properties of weaklydegenerate semiconductors at high frequencies and/or in the presence of a steady uniform magnetic field, when conditions are such that ionic scattering predominates over scattering by thermal agitation or by neutral impurities. Their applications and properties are discussed, and various expansions and relationships to other functions developed. The integrals are tabulated for argumentsx=0(.002).01.02(.02).1(.1)1(.2)2(.5)5(1)10(2)20 at half-integer spacings of the orderp.