  
| 
 | 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   http://functions.wolfram.com/07.32.03.0073.01
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
 | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
    HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], Subscript[a, q]}, 
  {Subscript[a, 1] + 1, \[Ellipsis], Subscript[a, q] + 1}, z] == 
 (1/Product[Gamma[Subscript[a, k] + 1], {k, 1, q}]) 
  Sum[Gamma[Subscript[a, k] + 1] Hypergeometric1F1Regularized[
     Subscript[a, k], Subscript[a, k] + 1, z] 
    Product[If[j == k, 1, Subscript[a, j]/(Subscript[a, j] - 
        Subscript[a, k])], {j, 1, q}], {k, 1, q}] 
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "q"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "+", "1"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "q"], "+", "1"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "k"], "+", "1"]], "]"]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "q"], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "k"], "+", "1"]], "]"]], RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[SubscriptBox["a", "k"], ",", RowBox[List[SubscriptBox["a", "k"], "+", "1"]], ",", "z"]], "]"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["If", "[", RowBox[List[RowBox[List["j", "\[Equal]", "k"]], ",", "1", ",", FractionBox[SubscriptBox["a", "j"], RowBox[List[SubscriptBox["a", "j"], "-", SubscriptBox["a", "k"]]]]]], "]"]]]]]]]]]]]]]] 
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
  
  | 
 
  | 
   
   <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>  <mi> q </mi>  </msub>  <msub>  <mover>  <mi> F </mi>  <mo> ~ </mo>  </mover>  <mi> q </mi>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <mo> … </mo>  <mo> , </mo>  <msub>  <mi> a </mi>  <mi> q </mi>  </msub>  </mrow>  <mo> ; </mo>  <mrow>  <mrow>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mo> … </mo>  <mo> , </mo>  <mrow>  <msub>  <mi> a </mi>  <mi> q </mi>  </msub>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["q", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "q"], HypergeometricPFQ, Rule[Editable, True]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "q"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mrow>  <mn> 1 </mn>  <mtext>   </mtext>  </mrow>  <mrow>  <munderover>  <mo> ∏ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mi> q </mi>  </munderover>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msub>  <mi> a </mi>  <mi> k </mi>  </msub>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mi> q </mi>  </munderover>  <mrow>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msub>  <mi> a </mi>  <mi> k </mi>  </msub>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <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>  <msub>  <mi> a </mi>  <mi> k </mi>  </msub>  <mo> ; </mo>  <mrow>  <msub>  <mi> a </mi>  <mi> k </mi>  </msub>  <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[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[SubscriptBox["a", "k"], Hypergeometric1F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[SubscriptBox["a", "k"], "+", "1"]], 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>  <munderover>  <mo> ∏ </mo>  <munder>  <mrow>  <mi> j </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mrow>  <mi> j </mi>  <mo> ≠ </mo>  <mi> k </mi>  </mrow>  </munder>  <mi> q </mi>  </munderover>  <mfrac>  <msub>  <mi> a </mi>  <mi> j </mi>  </msub>  <mrow>  <msub>  <mi> a </mi>  <mi> j </mi>  </msub>  <mo> - </mo>  <msub>  <mi> a </mi>  <mi> k </mi>  </msub>  </mrow>  </mfrac>  </mrow>  </mrow>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> FormBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> TagBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms>  </ms>  <apply>  <ci> FormBox </ci>  <ms> q </ms>  <ci> TraditionalForm </ci>  </apply>  </apply>  <apply>  <ci> SubscriptBox </ci>  <apply>  <ci> OverscriptBox </ci>  <ms> F </ms>  <ms> ~ </ms>  </apply>  <apply>  <ci> FormBox </ci>  <ms> q </ms>  <ci> TraditionalForm </ci>  </apply>  </apply>  </list>  </apply>  <ms> ⁡ </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> ( </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> TagBox </ci>  <apply>  <ci> ErrorBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> TagBox </ci>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> 1 </ms>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <ms> , </ms>  <apply>  <ci> TagBox </ci>  <ms> … </ms>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <ms> , </ms>  <apply>  <ci> TagBox </ci>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> q </ms>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  </list>  </apply>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <ms> ; </ms>  <apply>  <ci> TagBox </ci>  <apply>  <ci> TagBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> TagBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> 1 </ms>  </apply>  <ms> + </ms>  <ms> 1 </ms>  </list>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <ms> , </ms>  <apply>  <ci> TagBox </ci>  <ms> … </ms>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <ms> , </ms>  <apply>  <ci> TagBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> q </ms>  </apply>  <ms> + </ms>  <ms> 1 </ms>  </list>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  </list>  </apply>  <apply>  <ci> InterpretTemplate </ci>  <apply>  <ci> Function </ci>  <list>  <apply>  <ci> SlotSequence </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  </apply>  </apply>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <ms> ; </ms>  <apply>  <ci> TagBox </ci>  <ms> z </ms>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  </list>  </apply>  <ms> ) </ms>  </list>  </apply>  </list>  </apply>  <apply>  <ci> Function </ci>  <ci> Null </ci>  <apply>  <ci> HoldComplete </ci>  <apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Slot </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Slot </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <ci> Slot </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <list>  <ci> HoldAllComplete </ci>  </list>  </apply>  </apply>  <ms> ⩵ </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> FractionBox </ci>  <ms> 1 </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> UnderoverscriptBox </ci>  <ms> ∏ </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> k </ms>  <ms> = </ms>  <ms> 1 </ms>  </list>  </apply>  <ms> q </ms>  </apply>  <apply>  <ci> RowBox </ci>  <list>  <ms> Γ </ms>  <ms> ( </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> k </ms>  </apply>  <ms> + </ms>  <ms> 1 </ms>  </list>  </apply>  <ms> ) </ms>  </list>  </apply>  </list>  </apply>  </apply>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> UnderoverscriptBox </ci>  <ms> ∑ </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> k </ms>  <ms> = </ms>  <ms> 1 </ms>  </list>  </apply>  <ms> q </ms>  </apply>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <ms> Γ </ms>  <ms> ( </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> k </ms>  </apply>  <ms> + </ms>  <ms> 1 </ms>  </list>  </apply>  <ms> ) </ms>  </list>  </apply>  <apply>  <ci> TagBox </ci>  <apply>  <ci> TagBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms>  </ms>  <apply>  <ci> FormBox </ci>  <ms> 1 </ms>  <ci> TraditionalForm </ci>  </apply>  </apply>  <apply>  <ci> SubscriptBox </ci>  <apply>  <ci> OverscriptBox </ci>  <ms> F </ms>  <ms> ~ </ms>  </apply>  <apply>  <ci> FormBox </ci>  <ms> 1 </ms>  <ci> TraditionalForm </ci>  </apply>  </apply>  </list>  </apply>  <ms> ⁡ </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> ( </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> TagBox </ci>  <apply>  <ci> TagBox </ci>  <apply>  <ci> TagBox </ci>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> k </ms>  </apply>  <ci> Hypergeometric1F1Regularized </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <apply>  <ci> InterpretTemplate </ci>  <apply>  <ci> Function </ci>  <list>  <apply>  <ci> SlotSequence </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  </apply>  </apply>  </apply>  <ci> Hypergeometric1F1Regularized </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <false />  </apply>  </apply>  <ms> ; </ms>  <apply>  <ci> TagBox </ci>  <apply>  <ci> TagBox </ci>  <apply>  <ci> TagBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> k </ms>  </apply>  <ms> + </ms>  <ms> 1 </ms>  </list>  </apply>  <ci> Hypergeometric1F1Regularized </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <apply>  <ci> InterpretTemplate </ci>  <apply>  <ci> Function </ci>  <list>  <apply>  <ci> SlotSequence </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  </apply>  </apply>  </apply>  <ci> Hypergeometric1F1Regularized </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <false />  </apply>  </apply>  <ms> ; </ms>  <apply>  <ci> TagBox </ci>  <ms> z </ms>  <ci> Hypergeometric1F1Regularized </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  </list>  </apply>  <ms> ) </ms>  </list>  </apply>  </list>  </apply>  <apply>  <ci> InterpretTemplate </ci>  <apply>  <ci> Function </ci>  <apply>  <ci> HypergeometricPFQRegularized </ci>  <apply>  <ci> Slot </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Slot </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <ci> Slot </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <false />  </apply>  </apply>  <ci> Hypergeometric1F1Regularized </ci>  </apply>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> UnderoverscriptBox </ci>  <ms> ∏ </ms>  <apply>  <ci> UnderscriptBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <ms> j </ms>  <ms> = </ms>  <ms> 1 </ms>  </list>  </apply>  <apply>  <ci> RowBox </ci>  <list>  <ms> j </ms>  <ms> ≠ </ms>  <ms> k </ms>  </list>  </apply>  </apply>  <ms> q </ms>  </apply>  <apply>  <ci> FractionBox </ci>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> j </ms>  </apply>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> j </ms>  </apply>  <ms> - </ms>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> k </ms>  </apply>  </list>  </apply>  </apply>  </list>  </apply>  </list>  </apply>  </list>  </apply>  </list>  </apply>  </list>  </apply>  <ci> TraditionalForm </ci>  </apply>  </annotation-xml>  </semantics>  </math> 
   
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
 
  |   
  |  
  |  
  |   
  |  |  
  |   
  |  
  |  
  |   
  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "q_"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a_", "1"], "+", "1"]], ",", "\[Ellipsis]_", ",", RowBox[List[SubscriptBox["a_", "q_"], "+", "1"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "q"], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "k"], "+", "1"]], "]"]], " ", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[SubscriptBox["a", "k"], ",", RowBox[List[SubscriptBox["a", "k"], "+", "1"]], ",", "z"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["If", "[", RowBox[List[RowBox[List["j", "\[Equal]", "k"]], ",", "1", ",", FractionBox[SubscriptBox["a", "j"], RowBox[List[SubscriptBox["a", "j"], "-", SubscriptBox["a", "k"]]]]]], "]"]]]]]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "k"], "+", "1"]], "]"]]]]]]]]]  |  
  |  
  |   
  |  
  |  
  | 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   Date Added to functions.wolfram.com (modification date)
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
 | 
  | 
  
  
  
 |  
 
 |