Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7096)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-23/4

http://functions.wolfram.com/07.22.03.7096.01

Input Form

HypergeometricPFQ[{4}, {-(23/4), 19/4}, z] == (1/(21479424 z^(15/4))) ((-48 E^(2 Sqrt[z]) z^(3/4) (16804712925 + 4962157200 z + 663783120 z^2 + 50910208 z^3 + 2398464 z^4 + 45056 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-151242416325 + 302484832650 Sqrt[z] - 303932128500 z + 204551146800 z^(3/2) - 103783680000 z^2 + 42382660320 z^(5/2) - 14538363840 z^3 + 4324320000 z^(7/2) - 1141620480 z^4 + 269068800 z^(9/2) - 55071744 z^5 + 9105408 z^(11/2) - 1064960 z^6 + 65536 z^(13/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (151242416325 + 302484832650 Sqrt[z] + 303932128500 z + 204551146800 z^(3/2) + 103783680000 z^2 + 42382660320 z^(5/2) + 14538363840 z^3 + 4324320000 z^(7/2) + 1141620480 z^4 + 269068800 z^(9/2) + 55071744 z^5 + 9105408 z^(11/2) + 1064960 z^6 + 65536 z^(13/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 204551146800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 303932128500 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 302484832650 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 151242416325 </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]