Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7657)

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/07.22.03.7657.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), -(21/4)}, -z] == (1/4743512148375) (3 (1581170716125 - 314269956000 z + 54486432000 z^2 - 11921817600 z^3 + 4335206400 z^4 - 3963617280 z^5 + 38755368960 z^6 - 6218055680 z^7 + 35651584 z^8) - 4096 Sqrt[Pi] z^(25/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-65329605 + 9353760 z - 52480 z^2) Cos[2 Sqrt[z]] + 4 Sqrt[z] (10094505 - 254880 z + 256 z^2) Sin[2 Sqrt[z]]) - 4096 Sqrt[Pi] z^(25/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (4 Sqrt[z] (10094505 - 254880 z + 256 z^2) Cos[2 Sqrt[z]] + 5 (13065921 - 1870752 z + 10496 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]