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   http://functions.wolfram.com/07.21.03.0101.01
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    Hypergeometric1F1Regularized[a, a + 2, z] == 
 ((1 + a) E^z (-z)^a z + (a + z) (Gamma[2 + a] - (1 + a) Gamma[1 + a, -z]))/
  ((-z)^a (z Gamma[2 + a])) 
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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>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 1 </mn>  </msub>  <msub>  <mover>  <mi> F </mi>  <mo> ~ </mo>  </mover>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> ; </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 2 </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[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox["a", Hypergeometric1F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["a", "+", "2"]], Hypergeometric1F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False]], ";", TagBox["z", Hypergeometric1F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric1F1Regularized] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mo> - </mo>  <mi> a </mi>  </mrow>  </msup>  <mtext>   </mtext>  </mrow>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mi> z </mi>  </msup>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mi> a </mi>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> - </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> Hypergeometric1F1Regularized </ci>  <ci> a </ci>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <apply>  <power />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> a </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <ci> z </ci>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <power />  <exponentiale />  <ci> z </ci>  </apply>  <ci> z </ci>  <apply>  <power />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  <ci> a </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <ci> a </ci>  <ci> z </ci>  </apply>  <apply>  <plus />  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List["a_", ",", RowBox[List["a_", "+", "2"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], "a"], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["2", "+", "a"]], "]"]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "a"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["z", " ", RowBox[List["Gamma", "[", RowBox[List["2", "+", "a"]], "]"]]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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| HypergeometricPFQRegularized[{},{b},z] |  | HypergeometricPFQRegularized[{a1,a2},{b1},z] |  | HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] |  |   |  
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