Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7778)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-13/4

http://functions.wolfram.com/07.22.03.7778.01

Input Form

HypergeometricPFQ[{6}, {-(13/4), 17/4}, z] == (1/(31457280 z^(13/4))) ((8 E^(2 Sqrt[z]) z^(1/4) (-127702575 - 75093480 z - 25613280 z^2 - 10556160 z^3 - 1044480 z^4 + 229376 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (127702575 - 255405150 Sqrt[z] + 279417600 z - 218295000 z^(3/2) + 139708800 z^2 - 79168320 z^(5/2) + 49674240 z^3 - 36812160 z^(7/2) + 20697600 z^4 - 4730880 z^(9/2) - 1622016 z^5 + 950272 z^(11/2) + 131072 z^6) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (127702575 + 255405150 Sqrt[z] + 279417600 z + 218295000 z^(3/2) + 139708800 z^2 + 79168320 z^(5/2) + 49674240 z^3 + 36812160 z^(7/2) + 20697600 z^4 + 4730880 z^(9/2) - 1622016 z^5 - 950272 z^(11/2) + 131072 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </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]