汇总工具

调用顺序 参数 描述 示例

调用顺序 超铀(单位,L（左）,z（z）,n个) 超总和(单位,L（左）,z（z）,n个) 参数 U、 L（左） - 上下参数列表 z（z） - 评价点 n个 - 名称，重复变量 描述 • 此函数是Zeilberger-Koepf算法的实现，并计算总和的闭合形式 $\underset{\mathrm{<trans\; data-src="k">k个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}<trans\; data-src=""></trans>\mathrm{<trans\; data-src="hyperterm">肥大的</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="U">单位</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="L">L（左）</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="k">k个</trans>}\right)$    所有整数的总和k个，关于n个当Zeilberger算法的扩展给出合适的递推方程时。在这里，单位和L（左）表示上下参数列表，以及z（z）是评估点。的参数单位和L（左）假设与n个.程序超总和是未评估的相应惰性形式。 • 带有（sumtools，hypersum）的命令允许使用此命令的缩写形式。 示例 >  $\mathrm{<trans\; data-src="with">具有</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="sumtools">汇总工具</trans>}\right)<trans\; data-src="\&colon;">\&结肠；</trans>$ 道格尔的身份 >  $\mathrm{<trans\; data-src="hypersum">超铀</trans>}<trans\; data-src=""></trans>\left(\left[\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\frac{\mathrm{<trans\; data-src="a">一</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src=""></trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\&comma;">\&逗号；</trans><trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\left[\frac{\mathrm{<trans\; data-src="a">一</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\left(\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src=""></trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)$ $\frac{\mathrm{<trans\; data-src="pochhammer">pochhammer公司</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)<trans\; data-src=""></trans>\mathrm{<trans\; data-src="pochhammer">pochhammer公司</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)<trans\; data-src=""></trans>\mathrm{<trans\; data-src="pochhammer">pochhammer公司</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)\mathrm{<trans\; data-src="pochhammer">pochhammer公司</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)}{\mathrm{<trans\; data-src="pochhammer">pochhammer公司</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)<trans\; data-src=""></trans>\mathrm{<trans\; data-src="pochhammer">pochhammer公司</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)<trans\; data-src=""></trans>\mathrm{<trans\; data-src="pochhammer">pochhammer公司</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)<trans\; data-src=""></trans>\mathrm{<trans\; data-src="pochhammer">pochhammer公司</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)}$ (1) >  $\mathrm{<trans\; data-src="Hypersum">超总和</trans>}<trans\; data-src=""></trans>\left(\left[\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\frac{\mathrm{<trans\; data-src="a">一</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加；</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src=""></trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\&comma;">\&逗号；</trans><trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\left[\frac{\mathrm{<trans\; data-src="a">一</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\left(\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src=""></trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&plus;">\&加；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)$ $\mathrm{<trans\; data-src="Hyperterm">高血压</trans>}<trans\; data-src=""></trans>\left(\left[\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\left[\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="c">c（c）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="d">d日</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)$ (2) 安德鲁斯 >  $\mathrm{<trans\; data-src="Hypersum">超总和</trans>}<trans\; data-src=""></trans>\left(\left[<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="3">三</trans>}<trans\; data-src=""></trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="a">一</trans>}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\left[\frac{\mathrm{<trans\; data-src="3">三</trans>}\mathrm{<trans\; data-src="a">一</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="\&comma;">\&逗号；</trans>\frac{\mathrm{<trans\; data-src="3">三</trans>}<trans\; data-src=""></trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="\&plus;">\&加号；</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\frac{\mathrm{<trans\; data-src="3">三</trans>}}{\mathrm{<trans\; data-src="4">4</trans>}}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="n">n个</trans>}\right)$ $\left\{\begin{array}{cc}\mathrm{<trans\; data-src="Hyperterm">高血压</trans>}<trans\; data-src=""></trans>\left(\left[\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="3">三</trans>}}<trans\; data-src="\&comma;">\&逗号；</trans>\frac{\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="3">三</trans>}}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\left[\frac{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="3">三</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src="+">+</trans>\frac{\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="3">三</trans>}}\right]<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\frac{\mathrm{<trans\; data-src="n">n个</trans>}}{\mathrm{<trans\; data-src="3">三</trans>}}\right)& \mathrm{<trans\; data-src="irem">爱尔兰共和国</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="3">三</trans>}\right)<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}\\ \mathrm{<trans\; data-src="0">0</trans>}& \mathrm{<trans\; data-src="irem">爱尔兰共和国</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="3">三</trans>}\right)<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}\\ \mathrm{<trans\; data-src="0">0</trans>}& \mathrm{<trans\; data-src="irem">国际可再生能源管理局</trans>}<trans\; data-src=""></trans>\left(\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\&comma;">\&逗号；</trans>\mathrm{<trans\; data-src="3">三</trans>}\right)<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="2">2</trans>}\end{array}\right.$ (3) 另请参见 总和 汇总工具 SumTools[超几何][KoepfZeilberger]