Abstract
The integrals ∫ x 0 sin u / u du , ∫ x ∞ cos u / u du , ∫ ∞ -x e - u u / du called the sine-integral, cosine-integral, and exponential integral, were used by Schlömilch to express the values of several more complicated integrals, and denoted by him thus,—Si x , Ci x , Ei x ; the last function, however, is for all real values of x only another form of the logarithm-integral, the relation being Ei x =li e x . These functions have since been shown to be the key to a very large class of definite integrals, and several hundreds have been evaluated in terms of them by Schlömilch, De Haan, &c., so that for some time they have been considered primary functions of the integral calculus, and forms reduced to dependence on them have been regarded as known.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call