html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 JacobiP

 http://functions.wolfram.com/05.06.26.0016.01

 Input Form

 UnitStep[-1 + Abs[z]] (-1 + z)^(-1 - a - b - n) JacobiP[n, a, b, (1 + z)/(-1 + z)] == (((-1)^n Gamma[-a - b - n])/n!) MeijerG[{{-b - n, -a - b - n}, {}}, {{}, {0, -b}}, z]

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "z", "]"]]]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "a", "-", "b", "-", "n"]]], " ", RowBox[List["JacobiP", "[", RowBox[List["n", ",", "a", ",", "b", ",", FractionBox[RowBox[List["1", "+", "z"]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "n"]], "]"]]]], RowBox[List["n", "!"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "b"]], "-", "n"]], ",", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "n"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", RowBox[List["-", "b"]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]]]]]]]]

 MathML Form

 θ UnitStep ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" - 1 ) ( z - 1 ) - a - b - n - 1 P n ( a , b ) ( z + 1 z - 1 ) ( - 1 ) n Γ ( - a - b - n ) n ! G 2 , 2 0 , 2 ( z - b - n , - a - b - n 0 , - b ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "2"]], RowBox[List["0", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List[RowBox[List["-", "b"]], "-", "n"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "n"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", "b"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] θ UnitStep ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" - 1 ) ( z - 1 ) - a - b - n - 1 P n ( a , b ) ( z + 1 z - 1 ) ( - 1 ) n Γ ( - a - b - n ) n ! G 2 , 2 0 , 2 ( z - b - n , - a - b - n 0 , - b ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "2"]], RowBox[List["0", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List[RowBox[List["-", "b"]], "-", "n"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "n"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", "b"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z_"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "a_", "-", "b_", "-", "n_"]]], " ", RowBox[List["JacobiP", "[", RowBox[List["n_", ",", "a_", ",", "b_", ",", FractionBox[RowBox[List["1", "+", "z_"]], RowBox[List[RowBox[List["-", "1"]], "+", "z_"]]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "n"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "b"]], "-", "n"]], ",", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "n"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", RowBox[List["-", "b"]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["n", "!"]]]]]]]

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

 2001-10-29