Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8997)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8997.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 19/4}, -z] == (Sqrt[Pi] (61142922890124075 + 800416445107078800 z - 2439364404135859200 z^2 + 4336647829574860800 z^3 + 9461777082708787200 z^4 + 2018512444311207936 z^5 + 125911107637346304 z^6 + 2887593486188544 z^7 + 25164213387264 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (20380974296708025 - 123953319826801920 z + 196613972860032000 z^2 + 570522274447491072 z^3 + 124751671177641984 z^4 + 7836239419932672 z^5 + 180181461368832 z^6 + 1571958030336 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-61142922890124075 + 27686242058005440 z - 995493662392320 z^2 + 496954618288128000 z^3 + 119395998660427776 z^4 + 7705913305595904 z^5 + 179015981727744 z^6 + 1568736804864 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(9501201720202493952 z^(15/4))

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]