Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8058)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.8058.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(7/2), -(7/4)}, z] == (1/132300) ((-2 (-33075 - 66150 Sqrt[z] - 35100 z + 18000 z^(3/2) + 720 z^2 - 46080 z^(5/2) + 4650 z^3 - 45000 z^(7/2) - 10560 z^4 + 43776 z^(9/2) + 512 z^5 - 2048 z^(11/2) + E^(4 Sqrt[z]) (-33075 + 66150 Sqrt[z] - 35100 z - 18000 z^(3/2) + 720 z^2 + 46080 z^(5/2) + 4650 z^3 + 45000 z^(7/2) - 10560 z^4 - 43776 z^(9/2) + 512 z^5 + 2048 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (98325 + 104880 z - 88320 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (98325 + 104880 z - 88320 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 35100 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 66150 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -33075 </cn> </apply> </apply> <cn type='integer'> -33075 </cn> </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]