112 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



6.103 



Rn = 



6.104 Maclaurin's theorem: 



6.105 Lagrange's theorem. Given: 



y = z + 

 The expansion of f(y) in powers of x is: 



/() + ^WfW + J ^ [{*() 1VW] 



+ ..... + f, 



SYMBOLIC REPRESENTATION OF INFINITE SERIES 



6.150 The infinite series: 



ff \ - 2 _I 3 * k 



2l <h* f 3 ,03* f . . . + k{ a k x 

 may be written: 



/w = ", 



where a* is interpreted as equivalent to a*. 



6.151 The infinite series, written without factorials, 



f(x) = i -f aix + azx 2 + -f- ##* + . . . . 



may be written: 



i 



. i - ax 1 



where a k is interpreted as equivalent to a*. 



6.152 Symbolic form of Taylor's theorem: 



, 5 



6.153 Taylor's theorem for functions of many variables: 



^i 2 a 2 / , 2 

 - + 



