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variants of this functions
Hypergeometric0F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric0F1Regularized[b,z] > Identities > Functional identities > Relations between contiguous functions





http://functions.wolfram.com/07.18.17.0005.01









  


  








Input Form





Hypergeometric0F1Regularized[b - 1, z] - (b - 1) Hypergeometric0F1Regularized[b, z] z Hypergeometric0F1Regularized[ b + 1, z] == 0








Standard Form





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MathML Form







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</mo> <mi> z </mi> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 0 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mo> &#8202; </mo> <mo> ; </mo> <mrow> <mi> b </mi> <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[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;0&quot;, TraditionalForm]], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&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]]]]], Hypergeometric0F1Regularized, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[RowBox[List[&quot;b&quot;, &quot;+&quot;, &quot;1&quot;]], Hypergeometric0F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1Regularized, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, Hypergeometric0F1Regularized, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric0F1Regularized] </annotation> </semantics> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ci> Hypergeometric0F1Regularized </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Hypergeometric0F1Regularized </ci> <ci> b </ci> <ci> z </ci> </apply> <ci> z </ci> <apply> <ci> Hypergeometric0F1Regularized </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List[RowBox[List["b_", "-", "1"]], ",", "z_"]], "]"]], "-", RowBox[List[RowBox[List["(", RowBox[List["b_", "-", "1"]], ")"]], " ", RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List["b_", ",", "z_"]], "]"]], " ", "z_", " ", RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List[RowBox[List["b_", "+", "1"]], ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", "0"]]]]


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





2001-10-29