Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aagk)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.aagk.01

Input Form

HypergeometricPFQ[{-(5/4)}, {5/2, 19/4}, z] == -((1/(268435456 z^(15/4))) ((3 (4 z^(1/4) (-1334025 - 1778700 Sqrt[z] + 517440 z + 1774080 z^(3/2) - 171520 z^2 + 3205120 z^(5/2) + 1064960 z^3 - 4456448 z^(7/2) - 65536 z^4 + 262144 z^(9/2) + E^(4 Sqrt[z]) (1334025 - 1778700 Sqrt[z] - 517440 z + 1774080 z^(3/2) + 171520 z^2 + 3205120 z^(5/2) - 1064960 z^3 - 4456448 z^(7/2) + 65536 z^4 + 262144 z^(9/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (1334025 - 1940400 z + 8870400 z^2 + 15769600 z^3 - 18022400 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (1334025 - 1940400 z + 8870400 z^2 + 15769600 z^3 - 18022400 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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<times /> <cn type='integer'> 1940400 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1334025 </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> </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]