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variants of this functions
HypergeometricPFQRegularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > Representation of fundamental system solutions near point z==0 for p<=q+1 in the general case





http://functions.wolfram.com/07.32.13.0001.01









  


  








Input Form





D[Fold[Function[{f, k}, z D[f, z] + (Subscript[b, k] - 1) f], w[z], {1, \[Ellipsis], q}], z] - Fold[Function[{f, l}, z D[f, z] + Subscript[a, l] f], w[z], {1, \[Ellipsis], p}] == 0 /; (w[z] == Subscript[c, 1] HypergeometricPFQRegularized[ {Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] + Sum[Subscript[c, k + 1] z^(1 - Subscript[b, k]) HypergeometricPFQRegularized[{1 + Subscript[a, 1] - Subscript[b, k], \[Ellipsis], 1 + Subscript[a, p] - Subscript[b, k]}, {2 - Subscript[b, k], 1 + Subscript[b, 1] - Subscript[b, k], \[Ellipsis], 1 + Subscript[b, k - 1] - Subscript[b, k], 1 + Subscript[b, k + 1] - Subscript[b, k], \[Ellipsis], 1 + Subscript[b, q] - Subscript[b, k]}, z], {k, 1, q}] /; ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= q && 1 <= k <= q, !Element[Subscript[b, j] - Subscript[b, k], Integers]] && !Element[Subscript[b, k], Integers])








Standard Form





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MathML Form







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</ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> k </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <forall /> <bvar> <list> <ci> j </ci> <ci> k </ci> </list> </bvar> <bvar> <apply> <and /> <apply> <in /> <list> <ci> j </ci> <ci> k </ci> </list> <integers /> </apply> <apply> <neq /> <ci> j </ci> <ci> k </ci> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> j </ci> <ci> q </ci> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> k </ci> <ci> q </ci> </apply> </apply> </bvar> <apply> <notin /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> k </ci> </apply> </apply> </apply> <integers /> </apply> </apply> <apply> <notin /> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> k </ci> </apply> <integers /> </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