Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8214)

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`=-1/2

http://functions.wolfram.com/07.22.03.8214.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 5/4}, z] == (1/(469263974400 z^(1/4))) ((4 z^(1/4) (13481690625 + 57080918700 Sqrt[z] + 126900905040 z - 646639283520 z^(3/2) - 61724136960 z^2 + 262807418880 z^(5/2) + 5793423360 z^3 - 23621173248 z^(7/2) - 152764416 z^4 + 614203392 z^(9/2) + 1048576 z^5 - 4194304 z^(11/2) + E^(4 Sqrt[z]) (13481690625 - 57080918700 Sqrt[z] + 126900905040 z + 646639283520 z^(3/2) - 61724136960 z^2 - 262807418880 z^(5/2) + 5793423360 z^3 + 23621173248 z^(7/2) - 152764416 z^4 - 614203392 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-45176306175 - 481880599200 z + 2753603424000 z^2 - 1068064358400 z^3 + 94939054080 z^4 - 2459959296 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-45176306175 - 481880599200 z + 2753603424000 z^2 - 1068064358400 z^3 + 94939054080 z^4 - 2459959296 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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/> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1068064358400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2753603424000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 481880599200 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -45176306175 </cn> </apply> <apply> <ci> Erf </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> 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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]