Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8439)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8439.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(11/4)}, -z] == (-2 Sqrt[z] (118587803709375 - 8854556010300 z + 5782567190400 z^2 - 870537507840 z^3 + 158049239040 z^4 - 53497036800 z^5 + 66714599424 z^6 + 3537895424 z^7 + 33554432 z^8) Cos[2 Sqrt[z]] - 2097152 Sqrt[Pi] z^(29/4) (533577 + 27232 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (118587803709375 - 166971627622800 z - 24575910559200 z^2 + 4535346816000 z^3 - 704323952640 z^4 + 165315870720 z^5 - 93874814976 z^6 + 554252107776 z^7 + 28504489984 z^8 + 268435456 z^9) Sin[2 Sqrt[z]])/(52060747939200 z^(7/2))

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]