Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adr7)

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

For fixed z and a₁=11/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.adr7.01

Input Form

HypergeometricPFQ[{11/4}, {-(9/2), 19/4}, -z] == -((1/(264241152 z^(15/4))) (11 (3179665125 Sqrt[Pi] (363 + 16 z) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (28 Sqrt[z] (54962782875 - 22703241600 z + 2953267200 z^2 - 154632192 z^3 + 2621440 z^4) Cos[2 Sqrt[z]] + (-1154218440375 + 1180291694400 z - 258410880000 z^2 + 21202944000 z^3 - 677117952 z^4 + 4194304 z^5) 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]