134 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



Darling (Quarterly Journal, 49, p. 36, 1920) has obtained an approximation 

 to this integral: 



^--?- tan- 1 



FresnePs Integrals: 



6.701 





. 



6.702 



o ^ (2k + i) ! (4* + 3) 



k = o 



= o 



6.703 



R7ru 



6.704 



1 



f ^-gift = T^ (-!) 

 J I + / 6 ^^ y 



n = o 



x r^-Hi-o*- 1 



77 - r-. I - -7 

 ( - i) ! J i - xP 



o + w6) (a + w6 + i) (a + nb + 2) . . . (a + nb + k - i) 



p>>o, 



(Special cases, 6.445 and 6.922). 



6.705 



o w!(w + >') J y(y + i) . . . (y+n) 



n= o n=o 



6.706 If the sum of the series, 



/O) = 



is known, then 







(a + 



nb) (a + nb + i) (a + nb + 2) ..... (a + nb + k - i) 



n= o 



