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Bessel-integral functions

1933; Cambridge University Press; Volume: 3; Issue: 4 Linguagem: Inglês

10.1017/s0013091500027358

1464-3839

Pierre Humbert,

History and Theory of Mathematics

Summary In a very remarkable work on the operational Calculus, Dr Balth. van der Pol has introduced a new function, playing with respect to Bessel function of order zero the same part as the cosine- or sine-integral with respect to the ordinary cosine or sine. He showed that this function—which he called Bessel-integral junction —can be used to express the differential coefficient of any Bessel function with respect to its index. But he did not investigate the further properties of his new function. I propose to give here some of them, which appear to be interesting, and to introduce and study the functions connected, in the same way, with Bessel functions of any order.