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 | | http://functions.wolfram.com/07.20.17.0012.01 | 
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 | | a b (b - 1 + z) Hypergeometric1F1[a + 1, b, z] + 
  (1 - b) b (a + z) Hypergeometric1F1[a, b - 1, z] + 
  (a - b) (1 + a - b) z Hypergeometric1F1[a, b + 1, z] == 0 | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["a", " ", "b", " ", RowBox[List["(", RowBox[List["b", "-", "1", "+", "z"]], ")"]], " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List[RowBox[List["a", "+", "1"]], ",", "b", ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "b"]], ")"]], " ", "b", RowBox[List["(", RowBox[List["a", "+", "z"]], ")"]], " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List["a", ",", RowBox[List["b", "-", "1"]], ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", "a", "-", "b"]], ")"]], " ", "z", " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List["a", ",", RowBox[List["b", "+", "1"]], ",", "z"]], "]"]]]]]], "\[Equal]", "0"]]]] | 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mrow>  <mrow>  <mi> a </mi>  <mo> ⁢ </mo>  <mi> b </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 1 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ; </mo>  <mi> b </mi>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List["a", "+", "1"]], Hypergeometric1F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["b", Hypergeometric1F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False]], ";", TagBox["z", Hypergeometric1F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric1F1] </annotation>  </semantics>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> b </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> b </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 1 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> ; </mo>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox["a", Hypergeometric1F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["b", "-", "1"]], Hypergeometric1F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False]], ";", TagBox["z", Hypergeometric1F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric1F1] </annotation>  </semantics>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mi> b </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mi> b </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 1 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> ; </mo>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox["a", Hypergeometric1F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["b", "+", "1"]], Hypergeometric1F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False]], ";", TagBox["z", Hypergeometric1F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric1F1] </annotation>  </semantics>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mn> 0 </mn>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <plus />  <apply>  <times />  <ci> a </ci>  <ci> b </ci>  <apply>  <plus />  <ci> b </ci>  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <ci> Hypergeometric1F1 </ci>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <ci> b </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  </apply>  <ci> b </ci>  <apply>  <plus />  <ci> a </ci>  <ci> z </ci>  </apply>  <apply>  <ci> Hypergeometric1F1 </ci>  <ci> a </ci>  <apply>  <plus />  <ci> b </ci>  <cn type='integer'> -1 </cn>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <ci> a </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  </apply>  <apply>  <plus />  <ci> a </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <ci> z </ci>  <apply>  <ci> Hypergeometric1F1 </ci>  <ci> a </ci>  <apply>  <plus />  <ci> b </ci>  <cn type='integer'> 1 </cn>  </apply>  <ci> z </ci>  </apply>  </apply>  </apply>  <cn type='integer'> 0 </cn>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", "b_", " ", RowBox[List["(", RowBox[List["b_", "-", "1", "+", "z_"]], ")"]], " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List[RowBox[List["a_", "+", "1"]], ",", "b_", ",", "z_"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "b_"]], ")"]], " ", "b_", " ", RowBox[List["(", RowBox[List["a_", "+", "z_"]], ")"]], " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List["a_", ",", RowBox[List["b_", "-", "1"]], ",", "z_"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a_", "-", "b_"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", "a_", "-", "b_"]], ")"]], " ", "z_", " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List["a_", ",", RowBox[List["b_", "+", "1"]], ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", "0"]]]] | 
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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[{a1},{b1,b2},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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