Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7690)

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/07.22.03.7690.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), 1/4}, z] == (1/400982400) ((24 E^(2 Sqrt[z]) (16707600 + 82613925 z - 22362480 z^2 - 6218960 z^3 + 1515520 z^4 + 77824 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (-476974575 + 953949150 Sqrt[z] - 545113800 z - 181704600 z^(3/2) + 335091600 z^2 - 88728480 z^(5/2) - 47825280 z^3 + 20136960 z^(7/2) + 8478720 z^4 + 942080 z^(9/2) + 32768 z^5) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] z^(3/4) (-476974575 - 953949150 Sqrt[z] - 545113800 z + 181704600 z^(3/2) + 335091600 z^2 + 88728480 z^(5/2) - 47825280 z^3 - 20136960 z^(7/2) + 8478720 z^4 - 942080 z^(9/2) + 32768 z^5) 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]