330 



REPORTS ON THE STATE OF SCIENCE, ETC. 



(B). For negative values of x, \( — a;)=2Io(0)— Io(a;), and again the recurrence 

 formula will give functions of higher order. Generally 





and l2i + i( — a;)= 



^in-p)\(2p + l)\ 



-l2„(*) 



+ l2«+l(») 



The results obtained from the recurrence formula were checked with those computed 

 from 



l,{-x) + Ux) = \/|(a;H 15r' + 45a:a+ 15)/360. 



The poljmomial in the bracket can be thrown into the form (a;-+5)" — 10(3a;^+ll), 

 which only requires a table of squares and cubes. 



A partial check was introduced by calculating I|,(a;-|-A), where h=Q-\, from I„(a;) 

 and its difiEerential coefficients I„_i(a:), I„_2(a'), &c. 



^/^ 



The Probability Integral le-*'''^* and its Integrals — contd. 



I 



