200 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



9.152 fx\" 



(2) r 



J v (x) = - t - / '*<<* 9 sm 2v (p-d(p. 



. I \ Jo 



If n is an integer: 



9.153 



i /* 7r 2 /" 



/2n (x) = / cos (x sin 0) cos (2n<t>)d<t> = - I 2 . 



9.154 ^ ^ 



c-i) n r 2(-i> A 



/2n(#) = / COS (X COS <p) COS (2^0)^0 = - I 2 



^ Jo 7T J o 



9.155 



/2n+i(^) = / sin (^ sin 0) sin (2w + i) <j> d<j> = I 2 



TTjo Ttjo 



9.156 



. . (_!)n p . 2( _ l)n p 



/SflW = / sm (* cos 0) cos ( 2W + l)0^0 = ^ I 2 



^" */o 7T ./o 



9.157 



i /* +7r i ^ 27r 



J n (x) = I 6- tn *+* sm *d0 = I e -in0+ixsin0^A t 



2TTJ-TT 27Tj 



INTEGRAL PROPERTIES 



9.160 If C V (IJLX) is any one of the particular integrals: 



of the differential equation: 



d?y idy 



9.161 If /z* and /ij are two different roots of 



G(M^) = o, 



v (nix)x dx = a 



jf C v 



9.162 If /i* and jitz are two different roots of 



If 



^ 

 J 



= o, 



J C v (^ k x)C v (^x}xdx = ~ | ftCy*( Mfc &) - a 2 C, /2 (M^) - (a 2 - -^ ^ 



V r^k 



