Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7680)

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/07.22.03.7680.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), -(19/4)}, z] == (1/206239658625) ((E^(2 Sqrt[z]) (206239658625 + 49621572000 z + 10897286400 z^2 + 3251404800 z^3 + 1857945600 z^4 + 3963617280 z^5 - 15652546560 z^6 - 464584704 z^7 - 524288 z^8) - 256 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (49127715 + 32403780 Sqrt[z] + 7974240 z + 919680 z^(3/2) + 49920 z^2 + 1024 z^(5/2)) Erf[Sqrt[2] z^(1/4)] + 256 Sqrt[2 Pi] z^(23/4) (-49127715 + 32403780 Sqrt[z] - 7974240 z + 919680 z^(3/2) - 49920 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]