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Binomial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Binomial[n,k] > Summation > Multiple sums





http://functions.wolfram.com/06.03.23.0052.01









  


  








Input Form





Sum[(-1)^(k + l) Binomial[n, k] Binomial[n, n - k] Binomial[m, l] Binomial[m, m - l] Beta[n + m - k - l + 1, k + l + 1], {k, 0, n}, {l, 0, m}] == KroneckerDelta[n, m] ((2 n)!/n!^2) /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m >= 0








Standard Form





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MathML Form







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</mo> </mrow> <msup> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <sum /> <bvar> <ci> l </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> m </ci> </uplimit> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> k </ci> <ci> l </ci> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> k </ci> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> l </ci> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> l </ci> </apply> </apply> </apply> <apply> <ci> Beta </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> l </ci> </apply> <ci> m </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> k </ci> <ci> l </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> KroneckerDelta </ci> <ci> n </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <factorial /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <factorial /> <ci> n </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> <apply> <in /> <ci> m </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18