Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7783)

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=-11/4

http://functions.wolfram.com/07.22.03.7783.01

Input Form

HypergeometricPFQ[{6}, {-(11/4), -(9/4)}, -z] == (1/155925) (-3 (-51975 + 50400 z - 80640 z^2 + 1146880 z^3 - 489440 z^4 + 6144 z^5) + Sqrt[Pi] z^(13/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-5 (1708245 - 610848 z + 7424 z^2) Cos[2 Sqrt[z]] + 4 Sqrt[z] (2130345 - 124320 z + 256 z^2) Sin[2 Sqrt[z]]) + Sqrt[Pi] z^(13/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (4 Sqrt[z] (2130345 - 124320 z + 256 z^2) Cos[2 Sqrt[z]] + 5 (1708245 - 610848 z + 7424 z^2) Sin[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]