Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7750)

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=-15/4

http://functions.wolfram.com/07.22.03.7750.01

Input Form

HypergeometricPFQ[{6}, {-(15/4), -(1/4)}, z] == (1/6652800) ((-16 E^(2 Sqrt[z]) (-415800 - 2661120 z - 705285 z^2 + 1305540 z^3 + 328320 z^4 + 1024 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (-15663375 + 31326750 Sqrt[z] - 11138400 z - 19492200 z^(3/2) + 12852000 z^2 + 11424000 z^(5/2) + 2688000 z^3 + 251904 z^(7/2) + 8192 z^4) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] z^(5/4) (-15663375 - 31326750 Sqrt[z] - 11138400 z + 19492200 z^(3/2) + 12852000 z^2 - 11424000 z^(5/2) + 2688000 z^3 - 251904 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]