Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab20)

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ab20.01

Input Form

HypergeometricPFQ[{-(1/4)}, {-(11/2), 23/4}, z] == (19 (4 z^(1/4) (-1750949374048875 - 2334599165398500 Sqrt[z] - 1639913560084800 z - 763557636441600 z^(3/2) - 249288975936000 z^2 - 57532598323200 z^(5/2) - 9231761817600 z^3 - 977031659520 z^(7/2) - 68558192640 z^4 + 1502347264 z^(9/2) + E^(4 Sqrt[z]) (1750949374048875 - 2334599165398500 Sqrt[z] + 1639913560084800 z - 763557636441600 z^(3/2) + 249288975936000 z^2 - 57532598323200 z^(5/2) + 9231761817600 z^3 - 977031659520 z^(7/2) + 68558192640 z^4 + 1502347264 z^(9/2))) + 13923 E^(2 Sqrt[z]) Sqrt[2 Pi] (125759489625 - 16358958000 z + 1286208000 z^2 - 89088000 z^3 + 8192000 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - 13923 E^(2 Sqrt[z]) Sqrt[2 Pi] (125759489625 - 16358958000 z + 1286208000 z^2 - 89088000 z^3 + 8192000 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(3298534883328 z^(19/4))

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </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]