23 



V(0) = V'(0) = V"(0) = V(1) = V'(1) = V(m) = V'(m) = 



1 



jv(x)dx = i- 







1 

 W(0) = W'(0) = W"(0) = W(1) = W'd) = W'(m) = j W(x)cix = 







W(m) =-i- 



The procedure for determining these basic polynomials is similar to 

 that used for the sixth degree. Omitting the details of the calculations, we 

 have 



t = 2rQS^(x) + 2r^S^(x) + ^^'.v.) + CpV{x) + W(x) [53] 



where 



and 



S|^(x) = (a^ + Oj^x + agX^)x^(x - 1 )^(x - m)' 

 Sjx) = ()Sq +/S^x)x=^(x - 1)(x - m)2 

 U{x) = (y^ + y,x)x2{x - 1)2(x - m)^ 

 V(x) = ax3(x - 1)2(x - m)2 

 W(x) = (e^ + e.^ + e2X^)x''(x - 1)^ 



« = 2(1 + m) 

 1 I^ 



a^ ^_ 2(8 - 13m - 28m^ 4 63m^) 



^ ^ 15 - 40m + 28m^ 

 ° (1 - m)2D 



yS^ = _ 2(10 - 28m + 21m^) 

 (1 - m)2D 



^° "m^ 



[54] 



> [55] 



