Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8gl)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.a8gl.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(7/2), 19/4}, -z] == -((11 (Sqrt[Pi] (20461145079375 + 7183850310000 z + 1970427513600 z^2 + 834043392000 z^3 - 784982016000 z^4 + 115935805440 z^5 - 7633633280 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (6820381693125 - 723272004000 z + 66028435200 z^2 - 50658263040 z^3 + 7342325760 z^4 - 480247808 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (-20461145079375 + 14641371108000 z + 149432774400 z^2 - 58169180160 z^3 + 7755202560 z^4 - 492830720 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/ (14431090114560 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]