Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ac0o)

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=3/4, b_1`>=-11/2

For fixed z and a₁=3/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.ac0o.01

Input Form

HypergeometricPFQ[{3/4}, {-(7/2), 23/4}, -z] == -((1/(17179869184 z^(19/4))) (627 (3315 Sqrt[Pi] (1740902625 + 225086400 z + 16934400 z^2 + 1032192 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (2380 Sqrt[z] (-3233104875 + 1059973200 z - 79223040 z^2 + 1175552 z^3) Cos[2 Sqrt[z]] + (5771092201875 - 5409670266000 z + 823617849600 z^2 - 29247877120 z^3 + 134217728 z^4) 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]