264 



REPORTS ON THE STATE OF SCIENCE, ETC. 



The Series of Type I for S„(a;) and the Series of Type II for C„(a;) are absolutelj' 

 convergent for all values of m, n, x. 



The Series of Type I for C„(.t) is absolutely convergent for all values of n if x- —u > 

 and the Series of T.ype II for S„(.r) . for all values of n if x'^ + w > 0. 



These series are of great use for interpolation purposes and are far more serviceable 

 than the usual expansion by Taylor's Series : the latter involves the calculation of 

 the derivatives and this is a troublesome matter as a rule. Within the range < w < x, 

 it is best to use Type I for S„(a;) and Type II for C„(.r). 



Riccati-Bessel Functions. 



a;=0-l, 0-2, 0-9. 



