Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9318)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.9318.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(3/2), 5/4}, z] == (1/(530841600 z^(1/4))) ((4 z^(1/4) (4141125 + 49758300 Sqrt[z] - 2557440 z + 70744320 z^(3/2) + 29790720 z^2 - 128808960 z^(5/2) - 3440640 z^3 + 13959168 z^(7/2) + 65536 z^4 - 262144 z^(9/2) + E^(4 Sqrt[z]) (4141125 - 49758300 Sqrt[z] - 2557440 z - 70744320 z^(3/2) + 29790720 z^2 + 128808960 z^(5/2) - 3440640 z^3 - 13959168 z^(7/2) + 65536 z^4 + 262144 z^(9/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-62214075 - 237006000 z - 361152000 z^2 + 525312000 z^3 - 56033280 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-62214075 - 237006000 z - 361152000 z^2 + 525312000 z^3 - 56033280 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</cn> <apply> <times /> <cn type='integer'> 361152000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 237006000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -62214075 </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> </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]