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Binomial






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Binomial[n,k] > Inequalities





http://functions.wolfram.com/06.03.29.0004.01









  


  










Input Form





2 Subscript[d, n][\[Lambda] + \[Mu] + \[Nu] + \[Gamma]] Sum[(Subscript[d, n - k][\[Lambda]]/Subscript[d, k][ \[Mu] + \[Nu] + \[Gamma]]) Abs[Sum[Subscript[u, j] Subscript[v, k - j], {j, 0, k}] Sum[Subscript[x, j] Subscript[y, k - j], {j, 0, k}]], {k, 0, n}] <= Sum[(Subscript[d, n - k][\[Lambda] + \[Nu]]/Subscript[d, k][ \[Mu] + \[Gamma]]) Abs[Subscript[u, k]]^2, {k, 0, n}] Sum[(Subscript[d, n - k][\[Lambda] + \[Mu]]/Subscript[d, k][ \[Nu] + \[Gamma]]) Abs[Subscript[y, k]]^2, {k, 0, n}] Sum[(Subscript[d, n - k][\[Lambda] + \[Nu] + \[Gamma]]/ Subscript[d, k][\[Mu]]) Abs[Subscript[x, k]]^2, {k, 0, n}] Sum[(Subscript[d, n - k][\[Lambda] + \[Mu] + \[Gamma]]/ Subscript[d, k][\[Nu]]) Abs[Subscript[\[Nu], k]]^2, {k, 0, n}] /; Subscript[d, k][\[Alpha]] == Binomial[k + \[Alpha] - 1, k] && Element[\[Mu], Reals] && \[Mu] > 0 && Element[\[Nu], Reals] && \[Nu] > 0 && Element[\[Gamma], Reals] && \[Gamma] >= 0 && Element[\[Lambda], Reals] && \[Lambda] >= 0 && Max[Abs[{Subscript[u, 1], Subscript[u, 2], \[Ellipsis], Subscript[u, n]}]] > 0 && Max[Abs[{Subscript[v, 1], Subscript[v, 2], \[Ellipsis], Subscript[v, n]}]] > 0 && Max[Abs[{Subscript[x, 1], Subscript[x, 2], \[Ellipsis], Subscript[x, n]}]] > 0 && Max[Abs[{Subscript[y, 1], Subscript[y, 2], \[Ellipsis], Subscript[y, n]}]] > 0










Standard Form





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MathML Form







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</ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> k </ci> </apply> <apply> <plus /> <ci> &#947; </ci> <ci> &#956; </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <abs /> <apply> <ci> Subscript </ci> <ci> u </ci> <ci> k </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> d </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <plus /> <ci> &#955; </ci> <ci> &#956; </ci> </apply> </apply> <apply> <power /> <apply> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> k </ci> </apply> <apply> <plus /> <ci> &#947; </ci> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <abs /> <apply> <ci> Subscript </ci> <ci> y </ci> <ci> k </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> d </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <plus /> <ci> &#947; 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Rule Form





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





2002-12-18





© 1998- Wolfram Research, Inc.