Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa4m)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aa4m.01

Input Form

HypergeometricPFQ[{-(7/4)}, {11/2, 21/4}, z] == (1/(26843545600 z^(9/2))) ((-4 (-26011238400 + 12119043825 Sqrt[z] - 28431969300 z + 4605022800 z^(3/2) - 12957537600 z^2 + 1375234560 z^(5/2) - 4244244480 z^3 + 616734720 z^(7/2) - 2659614720 z^4 - 67829760 z^(9/2) + 274464768 z^5 + 1048576 z^(11/2) - 4194304 z^6 + E^(4 Sqrt[z]) (26011238400 + 12119043825 Sqrt[z] + 28431969300 z + 4605022800 z^(3/2) + 12957537600 z^2 + 1375234560 z^(5/2) + 4244244480 z^3 + 616734720 z^(7/2) + 2659614720 z^4 - 67829760 z^(9/2) - 274464768 z^5 + 1048576 z^(11/2) + 4194304 z^6)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (64141520625 + 94732092000 z + 46781280000 z^2 + 15353856000 z^3 + 10838016000 z^4 - 1101004800 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (64141520625 + 94732092000 z + 46781280000 z^2 + 15353856000 z^3 + 10838016000 z^4 - 1101004800 z^5 + 16777216 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> </apply> </apply> <apply> <times /> <cn type='integer'> 94732092000 </cn> <ci> z </ci> </apply> <cn type='integer'> 64141520625 </cn> </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]