XX. Tables of the numerical values of the sine-integral, cosine-integral, and exponential-integral

Abstract

Abstract It has for a long time been evident that the extension of the Integral Calculus would require the introduction of new functions; or, rather, that certain functions should be regarded as primary, so that forms reduced to dependence on them might be considered known. Thus, in the evaluation of Definite Integrals, the three transcendents ∫x0 sin u/udu, ∫x∞ cos u/udu, ∫-x∞ e-u/udu, called the sine-integral, the cosine-integral, and the exponential-integral, have become recognized elementary functions, and great use has been made of them to express the values of more complicated forms. They were introduced by Schlömilch to evaluate the integral ∫∞0a sin xθ/a2-θ2dθ, and several allied forms, and denoted by him Si x, Ci x, Ei x. Arndt also employed them in a similar manner about the same time.