Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af1x)

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.af1x.01

Input Form

HypergeometricPFQ[{17/4}, {-(11/2), 21/4}, -z] == -((1/(87199580160 z^(17/4))) (17 (-1012042268362125 Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (3 (337347422787375 - 359837250973200 z + 91387238342400 z^2 - 10225145548800 z^3 + 640722862080 z^4 - 24143462400 z^5 + 385875968 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (337347422787375 - 154215964702800 z + 24923792275200 z^2 - 2045029109760 z^3 + 100019404800 z^4 - 2689597440 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]