用牛顿二项式开平方

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用牛顿二项式开平方
通项公式为(1+Q)^(m/n)=1+ {m/n} *Q+ {(m/n)*(m/n-1)/2}*Q^2+{(m/n)*(m/n-1)*(m/n-2)/3*2}*Q^3....

比如要计算x^(1/2)
GO
(1+(x-1) )^(1/2)=1+ {1/2} *(x-1)+ {(1/2)*(1/2-1)/2}*(x-1)^2+{(1/2)*(1/2-1)*(1/2-2)/3*2}*(x-1)

^3....

(defun pow (num count)
(if (or (> count 1) (eq count 1))
      (* num
         (pow num
              (- count 1) ) )
      1))

(defun slist (count)
(if (or (> count 1) (eq count 1))
      (* count
         (slist (- count 1) ) )
      1))

(defun slistex (num count)
(if (or (> count 1) (eq count 1))
      (* num
         (slistex (- num 1) (- count 1) ) )
      1))

(defun expr (n exp rightvalue)
(if (> n 10)
       0
      (+ (expr (+ n 1)
                 exp
                 rightvalue)
          (* 1.0
              (pow rightvalue n)
              (/ (slistex exp n)
                  (slist n))))))

(expr 0 2 1)   2^2
(expr 0 3 1)   2^3
(expr 0 4 1)   2^4
(expr 0 2 2)   3^2
(expr 0 3 2)   3^3
(expr 0 4 2)   3^4
(expr 0 (/ 1.0 2) 1)   2^(1/2)

3^(1/2)
Go
{ 4 *(1-1/4) } ^(1/2)
Go
2*{ (1-1/4) } ^(1/2)
Go
(* 2 (expr 0 (/ 1.0 2) (/ -1.0 4) ) ) 3^(1/2)
如果直接用下面的方法是错误的，因为2^n是发散的
(expr 0 (/ 1.0 2) 2) 3^(1/2)

5^(1/2)
Go
{ 4 *(1+1/4) } ^(1/2)
Go
2*{ (1+1/4) } ^(1/2)
Go
(* 2 (expr 0 (/ 1.0 2) (/ 1.0 4) ) ) 5^(1/2)
如果直接用下面的方法是错误的，因为2^n是发散的
(expr 0 (/ 1.0 2) 2) 5^(1/2)