Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7664)

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/07.22.03.7664.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), -(5/4)}, z] == (1/454261500) ((12 E^(2 Sqrt[z]) (37855125 + 31600800 z + 93139200 z^2 + 68710740 z^3 - 27732320 z^4 + 5585920 z^5 + 98304 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (353296125 - 706592250 Sqrt[z] + 450355500 z + 41412000 z^(3/2) - 165404400 z^2 + 24360000 z^(5/2) + 35264000 z^3 + 7424000 z^(7/2) + 593920 z^4 + 16384 z^(9/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] z^(9/4) (-353296125 - 706592250 Sqrt[z] - 450355500 z + 41412000 z^(3/2) + 165404400 z^2 + 24360000 z^(5/2) - 35264000 z^3 + 7424000 z^(7/2) - 593920 z^4 + 16384 z^(9/2)) 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]