66 
variable is called 7,, then the series corresponding to Tarror’s 
series is: 
ry = fers) = flo) HIV 20), RAN. AD 
It can be of service in geometrical investigations of particular 
points. 
Whilst now a, cannot be developed in a series of sum, it is 
possible ta find a series of products: 
vp! 
Cx ik Ta Pp +1 (a). 
1 
é 
For the following development exists the limitation : 7 ER 
o P pl 
Let) = MA PED 
1 
$ 19. For a maxunum or minimum holds: 
Vay ss 
From series II ($ 18) follows, that in the immediate vicinity of 
the point the change of y depends on the factor: 
(rz), 2“ Ry 
whose first efficient is always greater than one, so that the second 
efficient decides whether in the point there is a maximum or a 
minimuin. 
For the second rational radix we find deduced: 
PR ver’, Ry :*( Ry). 
From this ensues as condition of an inflectional point 
hye Ty li hy) 
A rational inflectional point is characterized by 
Pity == 
In such a point the curve has with the touching rational 3 points 
in common. That now the two curves osculate each other follows 
easily from the equation of the rational ($ 7). 
y 
yf" — MA) 38 = Ry Or VEN SAR ae 
Kij 
so that the preceding condition is satisfied. 
The rational of contact in (@,, y¥,) is given by: 
y & 
a =a ’ Ry, 
Ni % 
