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   http://functions.wolfram.com/03.03.26.0117.01
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    BesselY[\[Nu], 2 Sqrt[z]] Hypergeometric0F1[-n + \[Nu], -z] == 
  ((2^(-1 - n) Gamma[-n + \[Nu]])/(z^(\[Nu]/2) Sqrt[Pi])) 
   (2^\[Nu] z^(\[Nu]/2) MeijerG[{{(1/2) (1 + n - \[Nu]), 
        (1/2) (2 + n - \[Nu])}, {1/2 + n - \[Nu]/2}}, 
      {{1 + n - \[Nu]/2, \[Nu]/2}, {1 + n - (3 \[Nu])/2, -(\[Nu]/2), 
        1/2 + n - \[Nu]/2}}, 4 z] - 2 Csc[\[Nu] Pi] 
     Sum[(((-1)^(k + Floor[(1 + n)/2]) 4^k z^k 
         Gamma[1/2 + k - n + Floor[n/2]])/(k! Gamma[1 + k - \[Nu]] 
         Gamma[k - n + \[Nu]])) Pochhammer[1 - k + Floor[n/2], 
        n - Floor[n/2]], {k, 0, Floor[n/2]}]) /; 
 Element[n, Integers] && n >= 0 
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   Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List[RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List[RowBox[List[RowBox[List["-", "n"]], "+", "\[Nu]"]], ",", RowBox[List["-", "z"]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["z", RowBox[List["-", FractionBox["\[Nu]", "2"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "n"]], "+", "\[Nu]"]], "]"]], " "]], SqrtBox["\[Pi]"]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "/", "2"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "n", "-", "\[Nu]"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "n", "-", "\[Nu]"]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], "+", "n", "-", FractionBox["\[Nu]", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", "n", "-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "n", "-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "2"]]], ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "+", "n", "-", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]], "-", RowBox[List["2", "  ", RowBox[List["Csc", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k", "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["1", "+", "n"]], "2"], "]"]]]]], " ", SuperscriptBox["4", "k"], " ", SuperscriptBox["z", "k"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "k", "-", "n", "+", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]], "]"]], " "]], RowBox[List[RowBox[List["k", "!"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "k", "-", "\[Nu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["k", "-", "n", "+", "\[Nu]"]], "]"]]]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "+", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]], ",", RowBox[List["n", "-", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]]]], "]"]]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "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>  <mrow>  <msub>  <mi> Y </mi>  <mi> ν </mi>  </msub>  <mo> ( </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 0 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mo>   </mo>  <mo> ; </mo>  <mrow>  <mi> ν </mi>  <mo> - </mo>  <mi> n </mi>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "0"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], 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</mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <msqrt>  <mi> π </mi>  </msqrt>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mn> 2 </mn>  <mi> ν </mi>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mi> ν </mi>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <semantics>  <mrow>  <msubsup>  <mi> G </mi>  <mrow>  <mn> 3 </mn>  <mo> , </mo>  <mn> 5 </mn>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> , </mo>  <mn> 2 </mn>  </mrow>  </msubsup>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ❘ </mo>  <mtable>  <mtr>  <mtd>  <mrow>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mi> ν </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> , </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mi> ν </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> , </mo>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mfrac>  <mi> ν </mi>  <mn> 2 </mn>  </mfrac>  <mo> + </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  </mrow>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mfrac>  <mi> ν </mi>  <mn> 2 </mn>  </mfrac>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mfrac>  <mi> ν </mi>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mfrac>  <mrow>  <mn> 3 </mn>  <mo> ⁢ </mo>  <mi> ν </mi>  </mrow>  <mn> 2 </mn>  </mfrac>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mi> ν </mi>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mfrac>  <mi> ν </mi>  <mn> 2 </mn>  </mfrac>  <mo> + </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  </mrow>  </mtd>  </mtr>  </mtable>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation 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</munderover>  <mfrac>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mi> k </mi>  <mo> + </mo>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mrow>  <mi> n </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mn> 2 </mn>  </mfrac>  <mo> ⌋ </mo>  </mrow>  </mrow>  </msup>  <mo> ⁢ </mo>  <msup>  <mn> 4 </mn>  <mi> k </mi>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mi> k </mi>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> - </mo>  <mi> n </mi>  <mo> + </mo>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mi> n </mi>  <mn> 2 </mn>  </mfrac>  <mo> ⌋ </mo>  </mrow>  <mo> + </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <semantics>  <msub>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> k </mi>  <mo> + </mo>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mi> n </mi>  <mn> 2 </mn>  </mfrac>  <mo> ⌋ </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mi> n </mi>  <mn> 2 </mn>  </mfrac>  <mo> ⌋ </mo>  </mrow>  </mrow>  </msub>  <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "k", "+", RowBox[List["\[LeftFloor]", FractionBox["n", "2"], "\[RightFloor]"]]]], ")"]], RowBox[List["n", "-", RowBox[List["\[LeftFloor]", FractionBox["n", "2"], "\[RightFloor]"]]]]], Pochhammer] </annotation>  </semantics>  </mrow>  <mrow>  <mrow>  <mi> k </mi>  <mo> ! </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> - </mo>  <mi> ν </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> - </mo>  <mi> n </mi>  <mo> + </mo>  <mi> ν </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> /; </mo>  <mrow>  <mi> n </mi>  <mo> ∈ </mo>  <semantics>  <mi> ℕ </mi>  <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation>  </semantics>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <eq />  <apply>  <times />  <apply>  <ci> BesselY </ci>  <ci> ν </ci>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Hypergeometric0F1 </ci>  <apply>  <plus />  <ci> ν </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> n </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> n </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <power />  <ci> z </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> ν </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> ν </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> n </ci>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <ci> ν </ci>  </apply>  <apply>  <power />  <ci> z </ci>  <apply>  <times />  <ci> ν </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> MeijerG </ci>  <list>  <list>  <apply>  <times />  <cn type='rational'> 1 <sep /> 2 </cn>  <apply>  <plus />  <ci> n </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> ν </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 2 </cn>  <apply>  <plus />  <ci> n </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> ν </ci>  </apply>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </list>  <list>  <apply>  <plus />  <ci> n </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> ν </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </list>  </list>  <list>  <list>  <apply>  <plus />  <ci> n </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> ν </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <times />  <ci> ν </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </list>  <list>  <apply>  <plus />  <ci> n </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 3 </cn>  <ci> ν </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> ν </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <plus />  <ci> n </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> ν </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </list>  </list>  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> z </ci>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <csc />  <apply>  <times />  <ci> ν </ci>  <pi />  </apply>  </apply>  <apply>  <sum />  <bvar>  <ci> k </ci>  </bvar>  <lowlimit>  <cn type='integer'> 0 </cn>  </lowlimit>  <uplimit>  <apply>  <floor />  <apply>  <times />  <ci> n </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </uplimit>  <apply>  <times />  <apply>  <power />  <cn type='integer'> -1 </cn>  <apply>  <plus />  <ci> k </ci>  <apply>  <floor />  <apply>  <times />  <apply>  <plus />  <ci> n </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <ci> k </ci>  </apply>  <apply>  <power />  <ci> z </ci>  <ci> k </ci>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> k </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> n </ci>  </apply>  <apply>  <floor />  <apply>  <times />  <ci> n </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <ci> Pochhammer </ci>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> k </ci>  </apply>  <apply>  <floor />  <apply>  <times />  <ci> n </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <plus />  <ci> n </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <floor />  <apply>  <times />  <ci> n </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <apply>  <factorial />  <ci> k </ci>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> k </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> ν </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> k </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> n </ci>  </apply>  <ci> ν </ci>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <in />  <ci> n </ci>  <integers />  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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