The integrals$\mathfrak{C}_p (x) = (p!)^{ - 1} \mathop \smallint \limits_0^\infty \varepsilon ^p (\varepsilon ^2 + x^2 )^{ - 1} e^{ - 6} d\varepsilon$ and$\mathfrak{D}_p (x) = (p!)^{ - 1} \mathop \smallint \limits_0^\infty \varepsilon ^p (\varepsilon ^2 + x^2 )^{ - 2} e^{ - 6} d\varepsilon$ and their tabulationand their tabulation

Summary

These integrals are fundamental to the theory of the properties of weakly-degenerate elemental semiconductors when conditions are such that ionic scattering is of comparable importance to scattering by thermal agitation and neutral impurities. Their applications and properties are discussed, and various expansions and relationships to other functions developed. The integrals are tabulated to four significant figures for the argumentsx=0 (.1) 1 (.2) 2 (.5) 10 (1) 20 at half-integer spacings of the orderp.