Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7662)

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=-23/4

http://functions.wolfram.com/07.22.03.7662.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), -(9/4)}, z] == (1/1022088375) ((E^(2 Sqrt[z]) (1022088375 + 474012000 z + 279417600 z^2 + 794787840 z^3 + 499554720 z^4 - 233055360 z^5 - 19271680 z^6 - 32768 z^7) - 2 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (-128118375 + 256236750 Sqrt[z] - 144698400 z - 52252200 z^(3/2) + 65076000 z^2 + 30624000 z^(5/2) + 4899840 z^3 + 333824 z^(7/2) + 8192 z^4) Erf[Sqrt[2] z^(1/4)] + 2 Sqrt[2 Pi] z^(13/4) (-128118375 - 256236750 Sqrt[z] - 144698400 z + 52252200 z^(3/2) + 65076000 z^2 - 30624000 z^(5/2) + 4899840 z^3 - 333824 z^(7/2) + 8192 z^4) 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]