Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7702)

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/07.22.03.7702.01

Input Form

HypergeometricPFQ[{6}, {-(19/4), -(17/4)}, z] == (1/9820936125) ((E^(2 Sqrt[z]) (9820936125 + 2918916000 z + 838252800 z^2 + 361267200 z^3 + 371589120 z^4 + 3963617280 z^5 + 837017600 z^6 + 6029312 z^7) + 64 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (36294225 + 25666980 Sqrt[z] + 6736800 z + 824960 z^(3/2) + 47360 z^2 + 1024 z^(5/2)) Erf[Sqrt[2] z^(1/4)] + 64 Sqrt[2 Pi] z^(21/4) (-36294225 + 25666980 Sqrt[z] - 6736800 z + 824960 z^(3/2) - 47360 z^2 + 1024 z^(5/2)) 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]