Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6892)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-15/4

http://functions.wolfram.com/07.22.03.6892.01

Input Form

HypergeometricPFQ[{3}, {-(15/4), 23/4}, z] == (1/(131072 z^(19/4))) ((19 (-16 E^(2 Sqrt[z]) z^(3/4) (1895268375 + 437451300 z + 41081040 z^2 + 1584000 z^3 + 20224 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-5685805125 + 11371610250 Sqrt[z] - 11059448400 z + 6956749800 z^(3/2) - 3171888720 z^2 + 1111350240 z^(5/2) - 308689920 z^3 + 68808960 z^(7/2) - 12222720 z^4 + 1669632 z^(9/2) - 159744 z^5 + 8192 z^(11/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (5685805125 + 11371610250 Sqrt[z] + 11059448400 z + 6956749800 z^(3/2) + 3171888720 z^2 + 1111350240 z^(5/2) + 308689920 z^3 + 68808960 z^(7/2) + 12222720 z^4 + 1669632 z^(9/2) + 159744 z^5 + 8192 z^(11/2)) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn 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]