Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afkn)

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.afkn.01

Input Form

HypergeometricPFQ[{19/4}, {-(7/2), 23/4}, -z] == (1/(880803840 z^(19/4))) (19 (-17313276605625 Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (60 Sqrt[z] (-384739480125 + 175880905200 z - 28425196800 z^2 + 2332323840 z^3 - 115146752 z^4 + 3145728 z^5) Cos[2 Sqrt[z]] + (17313276605625 - 18467495046000 z + 4690157472000 z^2 - 524772864000 z^3 + 32926924800 z^4 - 1274019840 z^5 + 16777216 z^6) 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]