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http://functions.wolfram.com/07.24.16.0009.01
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Hypergeometric2F1Regularized[a, b, c, g z] Hypergeometric2F1Regularized[
\[Alpha], \[Beta], \[Gamma], h z] == HypergeometricPFQRegularized[
{{}, {a, b}, {\[Alpha], \[Beta]}}, {{}, {c}, {\[Gamma]}}, g z, h z]
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Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a", ",", "b", ",", "c", ",", RowBox[List["g", " ", "z"]]]], "]"]], RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[List["h", " ", "z"]]]], "]"]]]], "\[Equal]", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]], ",", RowBox[List["{", RowBox[List["\[Alpha]", ",", "\[Beta]"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "c", "}"]], ",", RowBox[List["{", "\[Gamma]", "}"]]]], "}"]], ",", RowBox[List["g", " ", "z"]], ",", RowBox[List["h", " ", "z"]]]], "]"]]]]]]]]
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</mo> <mi> c </mi> <mo> ; </mo> <mrow> <mi> g </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox["b", Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["c", Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[RowBox[List["g", " ", "z"]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> α </mi> <mo> , </mo> <mi> β </mi> </mrow> <mo> ; </mo> <mi> γ </mi> <mo> ; </mo> <mrow> <mi> h </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["\[Alpha]", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox["\[Beta]", Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["\[Gamma]", Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[RowBox[List["h", " ", "z"]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] </annotation> </semantics> </mrow> <mo> ⩵ </mo> <mrow> <msubsup> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mrow> <mn> 0 </mn> <mo> ; 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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a_", ",", "b_", ",", "c_", ",", RowBox[List["g_", " ", "z_"]]]], "]"]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["\[Alpha]_", ",", "\[Beta]_", ",", "\[Gamma]_", ",", RowBox[List["h_", " ", "z_"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]], ",", RowBox[List["{", RowBox[List["\[Alpha]", ",", "\[Beta]"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "c", "}"]], ",", RowBox[List["{", "\[Gamma]", "}"]]]], "}"]], ",", RowBox[List["g", " ", "z"]], ",", RowBox[List["h", " ", "z"]]]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQRegularized[{},{b},z] | HypergeometricPFQRegularized[{a1},{b1},z] | HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] | |
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