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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Specific values > Values at z=1 > For fixed a1, a2, a3, a4, b1, b2, b3





http://functions.wolfram.com/07.28.03.0002.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, 1] == ((Gamma[Subscript[\[Psi], 3]] Product[Gamma[Subscript[b, k]], {k, 1, 3}])/Product[Gamma[Subscript[a, k]], {k, 3, 4}]) Sum[(Pochhammer[Subscript[\[Psi], 3], k] HypergeometricPFQExpansionCoefficient[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, k])/ (Gamma[Subscript[\[Psi], 3] + Subscript[a, 1] + k] Gamma[Subscript[\[Psi], 3] + Subscript[a, 2] + k]), {k, 0, Infinity}] /; Subscript[\[Psi], 3] == Sum[Subscript[b, j], {j, 1, 3}] - Sum[Subscript[a, j], {j, 1, 4}] && Re[Subscript[\[Psi], 3]] > 0 && Re[Subscript[a, 3]] > 0 && Re[Subscript[a, 4]] > 0










Standard Form





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MathML Form







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</mi> <mn> 3 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





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