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http://functions.wolfram.com/07.22.20.0009.01
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(D[HypergeometricPFQ[{1}, {b, b + 1/2}, z], b] /. b -> 1) ==
(1/Sqrt[z]) (CoshIntegral[2 Sqrt[z]] Sinh[2 Sqrt[z]] -
Cosh[2 Sqrt[z]] SinhIntegral[2 Sqrt[z]] -
(EulerGamma + Log[2] + Log[z]/2 - 1) Sinh[2 Sqrt[z]])
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["b_"]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["b_", ",", RowBox[List["b_", "+", FractionBox["1", "2"]]]]], "}"]], ",", "z_"]], "]"]]]], "/.", "\[InvisibleSpace]", RowBox[List["b_", "\[Rule]", "1"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["CoshIntegral", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]]]], "-", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["EulerGamma", "+", RowBox[List["Log", "[", "2", "]"]], "+", FractionBox[RowBox[List["Log", "[", "z", "]"]], "2"], "-", "1"]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]]]]]], SqrtBox["z"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
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