Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7704)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-19/4

http://functions.wolfram.com/07.22.03.7704.01

Input Form

HypergeometricPFQ[{6}, {-(19/4), -(13/4)}, z] == (1/577702125) ((E^(2 Sqrt[z]) (577702125 + 224532000 z + 93139200 z^2 + 72253440 z^3 + 371589120 z^4 - 528044160 z^5 - 22507520 z^6 - 32768 z^7) - 8 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (-18589725 + 37179450 Sqrt[z] + 35409000 z + 10616640 z^(3/2) + 1428480 z^2 + 88576 z^(5/2) + 2048 z^3) Erf[Sqrt[2] z^(1/4)] + 8 Sqrt[2 Pi] z^(17/4) (-18589725 - 37179450 Sqrt[z] + 35409000 z - 10616640 z^(3/2) + 1428480 z^2 - 88576 z^(5/2) + 2048 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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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]