Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8836)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.8836.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, 3/4}, z] == (1/16179609600) ((-4 (-2022451200 - 3127028625 Sqrt[z] + 16938954900 z + 2111739840 z^(3/2) - 9129093120 z^2 - 253048320 z^(5/2) + 1035847680 z^3 + 8110080 z^(7/2) - 32636928 z^4 - 65536 z^(9/2) + 262144 z^5 + E^(4 Sqrt[z]) (-2022451200 + 3127028625 Sqrt[z] + 16938954900 z - 2111739840 z^(3/2) - 9129093120 z^2 + 253048320 z^(5/2) + 1035847680 z^3 - 8110080 z^(7/2) - 32636928 z^4 + 65536 z^(9/2) + 262144 z^5)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (13749310575 - 73329656400 z + 37246809600 z^2 - 4167475200 z^3 + 130744320 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (-13749310575 + 73329656400 z - 37246809600 z^2 + 4167475200 z^3 - 130744320 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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<power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4167475200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 37246809600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 73329656400 </cn> <ci> z </ci> </apply> <cn type='integer'> -13749310575 </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]