ã¢ãã«ã¼ãã³é¢æ° \(A(x,y)\) ã¯ã´ã£ã«ãã«ã ã»ã¢ãã«ã¼ãã³ãå®ç¾©ãã¦ãã¼ã¿ã¼ã¨ããã³ã½ã³ãæ¡å¼µããå帰é¢æ°ã§ãããç¾å¨ã¯ããã³ã½ã³ã®å®ç¾©ãæåã¨ãªã£ã¦ãããã¢ãã«ã¼ãã³æ°ã¯ã¢ãã«ã¼ãã³é¢æ°ã®ãªãªã¸ãã«ã®å®ç¾©ã«ãã£ã¦å®ç¾©ã§ããã å®ç¾©[] ããã³ã½ã³ã®å®ç¾©[] 次ã®æ§ã«å®ç¾©ããã[1][2]ã 表示ããã¹ã¯ãããçã«åãæ¿ãã¦æ°å¼ã表示ããã éè² æ´æ° \(x,y\) ã«å¯¾ãã¦, \[ A(x,y)= \begin{cases} y+1 & \text{if}\ x=0, \\ A(x-1,1) & \text{if}\ x>0, y=0, \\ A(x-1,A(x,y-1)) & \text{otherwise}. \end{cases} \] ãããã£ã¦ãä¾ãã°æ¬¡ã®ããã«è¨ç®ãããã \begin{align*} A(1,2) \ &=\ A(0,A(1,1))\\ \ &=\
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