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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case 0F3





http://functions.wolfram.com/07.31.03.0098.01









  


  








Input Form





HypergeometricPFQ[{}, {1/2, b, b + 1/2}, z] + ((2 Sqrt[z])/b) HypergeometricPFQ[{}, {3/2, b + 1/2, b + 1}, z] == Hypergeometric0F1[2 b, 4 Sqrt[z]]








Standard Form





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MathML Form







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</mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 0 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mo> &#8202; </mo> <mo> ; </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> ; </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;0&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[&quot;\[Null]&quot;, InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;b&quot;]], Hypergeometric0F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;4&quot;, &quot; &quot;, SqrtBox[&quot;z&quot;]]], Hypergeometric0F1, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric0F1] </annotation> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ci> HypergeometricPFQ </ci> <list /> <list> <cn type='rational'> 1 <sep /> 2 </cn> <ci> b </ci> <apply> <plus /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list /> <list> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <plus /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </list> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> Hypergeometric0F1 </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29