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; }

 HypergeometricPFQRegularized

 http://functions.wolfram.com/07.32.20.0004.01

 Input Form

 Derivative[{0, \[Ellipsis], 0}, {1, 0, \[Ellipsis], 0}, 0][ HypergeometricPFQRegularized][{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == (-z) Gamma[Subscript[b, 1]] Product[Subscript[a, j] HypergeometricPFQRegularized[{{1 + Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, p]}, {1}, {1, Subscript[b, 1]}}, {{2, 1 + Subscript[b, 1], \[Ellipsis], 1 + Subscript[b, q]}, {}, {1 + Subscript[b, 1]}}, z, z], {j, 1, p}] - PolyGamma[Subscript[b, 1]] HypergeometricPFQRegularized[ {Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["Derivative", "[", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "\[Ellipsis]", ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "0", ",", "\[Ellipsis]", ",", "0"]], "}"]], ",", "0"]], "]"]], "[", "HypergeometricPFQRegularized", "]"]], "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["Gamma", "[", SubscriptBox["b", "1"], "]"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List[SubscriptBox["a", "j"], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "+", SubscriptBox["a", "p"]]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", SubscriptBox["b", "1"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["1", "+", SubscriptBox["b", "1"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "+", SubscriptBox["b", "q"]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["b", "1"]]], "}"]]]], "}"]], ",", "z", ",", "z"]], "]"]]]]]]]], "-", RowBox[List[RowBox[List["PolyGamma", "[", SubscriptBox["b", "1"], "]"]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]]]]]]]]]]

 MathML Form

 p F ~ q ( { 0 , , 0 } , { 1 , 0 , , 0 } , 0 ) ( a 1 , , a p TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; b 1 , , b q TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; z TagBox["z", HypergeometricPFQ, Rule[Editable, True]] ) - z Γ ( b 1 ) ( j = 1 p a j ) F ~ q + 1 0 1 p 1 2 ( a 1 + 1 , , a p + 1 ; 1 ; 1 , b 1 ; 2 , b 1 + 1 , , b q + 1 ; ; b 1 + 1 ; z , z ) - ψ TagBox["\[Psi]", PolyGamma] ( b 1 ) p F ~ q ( a 1 , , a p TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]] ; b 1 TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]] , TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]] , b q TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]] ; z TagBox["z", HypergeometricPFQ, Rule[Editable, True]] ) p F ~ q ( { 0 , , 0 } , { 1 , 0 , , 0 } , 0 ) ( a 1 , , a p TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; b 1 , , b q TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; z TagBox["z", HypergeometricPFQ, Rule[Editable, True]] ) - z Γ ( b 1 ) ( j = 1 p a j ) F ~ q + 1 0 1 p 1 2 ( a 1 + 1 , , a p + 1 ; 1 ; 1 , b 1 ; 2 , b 1 + 1 , , b q + 1 ; ; b 1 + 1 ; z , z ) - ψ TagBox["\[Psi]", PolyGamma] ( b 1 ) p F ~ q ( a 1 , , a p TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]] ; b 1 TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]] , TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]] , b q TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]] ; z TagBox["z", HypergeometricPFQ, Rule[Editable, True]] ) [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["HypergeometricPFQRegularized", TagBox[RowBox[List["(", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "\[Ellipsis]_", ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "0", ",", "\[Ellipsis]_", ",", "0"]], "}"]], ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["Gamma", "[", SubscriptBox["bb", "1"], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List[SubscriptBox["a", "j"], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["aa", "1"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "+", SubscriptBox["aa", "p"]]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", SubscriptBox["bb", "1"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "+", SubscriptBox["bb", "q"]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], "}"]]]], "}"]], ",", "z", ",", "z"]], "]"]]]]]]]], "-", RowBox[List[RowBox[List["PolyGamma", "[", SubscriptBox["bb", "1"], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["aa", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["bb", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "q"]]], "}"]], ",", "z"]], "]"]]]]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.