Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7683)

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/07.22.03.7683.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), -(15/4)}, -z] == (1/10854718875) (-7 (-1550674125 + 472586400 z - 141523200 z^2 + 66355200 z^3 - 88473600 z^4 + 394778880 z^5 - 112951296 z^6 + 851968 z^7) + 128 Sqrt[Pi] z^(19/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((26277615 + 45700200 z - 1605120 z^2 + 2048 z^3) Cos[2 Sqrt[z]] + 6 Sqrt[z] (8759205 - 2123040 z + 15616 z^2) Sin[2 Sqrt[z]]) + 128 Sqrt[Pi] z^(19/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-6 Sqrt[z] (8759205 - 2123040 z + 15616 z^2) Cos[2 Sqrt[z]] + (26277615 + 45700200 z - 1605120 z^2 + 2048 z^3) 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]