感叹号为阶乘的意思。
n!=1×2×3×...×n。
阶乘亦可以递归方式定义:0!=1,n!=(n-1)!×n。
双阶乘用“m!!”表示。
当 m 是自然数时,表示不超过 m 且与 m 有相同奇偶性的所有正整数的乘积。如:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/a8773912b31bb051be0d30e6387adab44bede0d7?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/902397dda144ad34f0af0449dea20cf430ad85e8?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
当 m 是负奇数时,表示绝对值小于它的绝对值的所有负奇数的绝对值积的倒数。
当 m 是负偶数时,m!!不存在。
扩展资料:
伽玛函数(Gamma Function)
定义伽马函数:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/3c6d55fbb2fb43161e16f9b42ea4462308f7d3f7?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
运用积分的知识,我们可以证明Γ(s)=(s-1)× Γ(s-1)
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/0bd162d9f2d3572c74321d128413632763d0c328?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/86d6277f9e2f07087c0ca9cee724b899a801f2f7?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
所以,当 x 是整数 n 时,
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/023b5bb5c9ea15cea0ed61c7b8003af33b87b2f9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
这样 Gamma 函数实际上就是阶乘的延拓。
参考资料来源:百度百科-阶乘