Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7682)

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=-21/4

http://functions.wolfram.com/07.22.03.7682.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), -(15/4)}, z] == (1/10854718875) ((7 E^(2 Sqrt[z]) (1550674125 + 472586400 z + 141523200 z^2 + 66355200 z^3 + 88473600 z^4 + 394778880 z^5 + 112951296 z^6 + 851968 z^7) + 32 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-26277615 + 52555230 Sqrt[z] + 45700200 z + 12738240 z^(3/2) + 1605120 z^2 + 93696 z^(5/2) + 2048 z^3) Erf[Sqrt[2] z^(1/4)] + 32 Sqrt[2 Pi] z^(19/4) (-26277615 - 52555230 Sqrt[z] + 45700200 z - 12738240 z^(3/2) + 1605120 z^2 - 93696 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]