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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/01.19.16.0112.01









  


  










Input Form





Product[Cosh[Subscript[z, k]], {k, 1, n}] == Sum[(-1)^Sum[(2*Subscript[k, j] + 2)/4, {j, 1, n}]* Sinh[Sum[Subscript[k, j] Subscript[z, j], {j, 1, n}]], {Subscript[k, 1], -1, 1, 2}, {Subscript[k, 2], -1, 1, 2}, …, {Subscript[k, n], -1, 1, 2}]/(-2)^n /; Element[(n + 1)/2, Integers] && n > 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["Sinh", "[", SubscriptBox["z", "k"], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["-", "n"]]], RowBox[List[UnderoverscriptBox["\[Sum]", UnderscriptBox[RowBox[List[SubscriptBox["k", "1"], "=", RowBox[List["-", "1"]]]], RowBox[List[RowBox[List["\[CapitalDelta]", " ", SubscriptBox["k", "1"]]], "=", "2"]]], "1"], RowBox[List[UnderoverscriptBox["\[Sum]", UnderscriptBox[RowBox[List[SubscriptBox["k", "2"], "=", RowBox[List["-", "1"]]]], RowBox[List[RowBox[List["\[CapitalDelta]", " ", SubscriptBox["k", "2"]]], "=", "2"]]], "1"], RowBox[List["\[Ellipsis]", RowBox[List[UnderoverscriptBox["\[Sum]", UnderscriptBox[RowBox[List[SubscriptBox["k", "n"], "=", RowBox[List["-", "1"]]]], RowBox[List[RowBox[List["\[CapitalDelta]", " ", SubscriptBox["k", "n"]]], "=", "2"]]], "1"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "n"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["k", "j"]]], "+", "2"]], ")"]], "/", "4"]]]]], RowBox[List["Sinh", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "n"], RowBox[List[SubscriptBox["k", "j"], SubscriptBox["z", "j"]]]]], "]"]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List[FractionBox[RowBox[List["n", "+", "1"]], "2"], "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]










MathML Form







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</ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> 2 </ms> </apply> <ms> &#8712; </ms> <apply> <ci> SuperscriptBox </ci> <ms> &#8469; </ms> <ms> + </ms> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










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





2002-12-18