Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9378)

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`=-1/2

http://functions.wolfram.com/07.22.03.9378.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(1/2), 17/4}, z] == (-4 z^(1/4) (-6005213589375 - 8006951452500 Sqrt[z] - 711729018000 z + 3931455528000 z^(3/2) - 1350744595200 z^2 - 4850849203200 z^(5/2) + 32154071040 z^3 - 10978275409920 z^(7/2) - 5926412943360 z^4 + 26240274923520 z^(9/2) + 948924579840 z^5 - 3891630440448 z^(11/2) - 32900120576 z^6 + 132405788672 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (-6005213589375 + 8006951452500 Sqrt[z] - 711729018000 z - 3931455528000 z^(3/2) - 1350744595200 z^2 + 4850849203200 z^(5/2) + 32154071040 z^3 + 10978275409920 z^(7/2) - 5926412943360 z^4 - 26240274923520 z^(9/2) + 948924579840 z^5 + 3891630440448 z^(11/2) - 32900120576 z^6 - 132405788672 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-6005213589375 + 5693832144000 z - 5797356364800 z^2 + 26502200524800 z^3 + 58893778944000 z^4 - 107691481497600 z^5 + 15664215490560 z^6 - 530428461056 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-6005213589375 + 5693832144000 z - 5797356364800 z^2 + 26502200524800 z^3 + 58893778944000 z^4 - 107691481497600 z^5 + 15664215490560 z^6 - 530428461056 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(173173081374720 z^(13/4))

Standard Form

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MathML Form

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</cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 107691481497600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 58893778944000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 26502200524800 </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'> 5797356364800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5693832144000 </cn> <ci> z </ci> </apply> <cn type='integer'> -6005213589375 </cn> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> 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</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]