def _d(n, j, prec, sq23pi, sqrt8):
 j = from_int(j)
 pi = mpf_pi(prec)
 a = mpf_div(sq23pi, j, prec)
 b = mpf_sub(from_int(n), from_rational(1, 24, prec), prec)
 c = mpf_sqrt(b, prec)
 (ch, sh) = mpf_cosh_sinh(mpf_mul(a, c), prec)
 D = mpf_div(mpf_sqrt(j, prec), mpf_mul(mpf_mul(sqrt8, b), pi), prec)
 E = mpf_sub(mpf_mul(a, ch), mpf_div(sh, c, prec), prec)
 return mpf_mul(D, E)

def _d ( n , j , prec , sq23pi , sqrt8 ) : j = from_int ( j ) pi = mpf_pi ( prec ) a = mpf_div ( sq23pi , j , prec ) b = mpf_sub ( from_int ( n ) , from_rational ( 1 , 24 , prec ) , prec ) c = mpf_sqrt ( b , prec ) ( ch , sh ) = mpf_cosh_sinh ( mpf_mul ( a , c ) , prec ) D = mpf_div ( mpf_sqrt ( j , prec ) , mpf_mul ( mpf_mul ( sqrt8 , b ) , pi ) , prec ) E = mpf_sub ( mpf_mul ( a , ch ) , mpf_div ( sh , c , prec ) , prec ) return mpf_mul ( D , E )
compute the sinh term in the outer sum of the hrr formula .