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   http://functions.wolfram.com/07.32.03.0123.01
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    HypergeometricPFQRegularized[{-n, n + 2, c, 2 - c}, {3/2}, z] == 
  ((Sqrt[Pi] (-1)^n Csc[c Pi])/(2 (c - 1) (1 + n) z)) 
   (BesselI[-c - n, 1/Sqrt[z]] BesselI[-2 + c - n, 1/Sqrt[z]] - 
    BesselI[2 - c + n, 1/Sqrt[z]] BesselI[c + n, 1/Sqrt[z]]) /; 
 Element[n, Integers] && n >= 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>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 4 </mn>  </msub>  <msub>  <mover>  <mi> F </mi>  <mo> ~ </mo>  </mover>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mi> n </mi>  </mrow>  <mo> , </mo>  <mrow>  <mi> n </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  <mo> , </mo>  <mi> c </mi>  <mo> , </mo>  <mrow>  <mn> 2 </mn>  <mo> - </mo>  <mi> c </mi>  </mrow>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", "n"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["n", "+", "2"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["c", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["2", "-", "c"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mrow>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mi> n </mi>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> csc </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> π </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> n </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <msub>  <mi> I </mi>  <mrow>  <mrow>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> - </mo>  <mi> n </mi>  </mrow>  </msub>  <mo> ( </mo>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mi> z </mi>  </msqrt>  </mfrac>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> I </mi>  <mrow>  <mi> c </mi>  <mo> - </mo>  <mi> n </mi>  <mo> - </mo>  <mn> 2 </mn>  </mrow>  </msub>  <mo> ( </mo>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mi> z </mi>  </msqrt>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <mrow>  <msub>  <mi> I </mi>  <mrow>  <mn> 2 </mn>  <mo> - </mo>  <mi> c </mi>  <mo> + </mo>  <mi> n </mi>  </mrow>  </msub>  <mo> ( </mo>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mi> z </mi>  </msqrt>  </mfrac>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> I </mi>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mi> n </mi>  </mrow>  </msub>  <mo> ( </mo>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mi> z </mi>  </msqrt>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> /; 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   Date Added to functions.wolfram.com (modification date)
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