Generalized hypergeometric function 1F2: Differential equations (formula 07.22.13.0014)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Differential equations

Ordinary linear differential equations and wronskians

For the direct function itself

http://functions.wolfram.com/07.22.13.0014.01

Input Form

Wronskian[s^z HypergeometricPFQRegularized[{Subscript[a, 1]}, {Subscript[b, 1], Subscript[b, 2]}, a r^z], s^z (MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2]}}, a r^z] + MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1]}}, a r^z]), s^z MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {}}, (-a) r^z], z] == a^3 r^(3 z) ((-a) r^z)^(-Subscript[b, 1] - Subscript[b, 2]) (a r^z)^(-1 - Subscript[b, 1] - Subscript[b, 2]) (((-a) r^z)^Subscript[b, 2] (a r^z)^Subscript[b, 1] + ((-a) r^z)^Subscript[b, 1] (a r^z)^Subscript[b, 2]) s^(3 z) Gamma[1 + Subscript[a, 1] - Subscript[b, 1]] Gamma[1 + Subscript[a, 1] - Subscript[b, 2]] Log[r]^3

Standard Form

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MathML Form

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</apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> s </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <ln /> <ci> r </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]