Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9171)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9171.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 1/4}, -z] == (1/23224320) (Sqrt[Pi] z^(3/4) (-76039425 + 46347840 z - 9192960 z^2 + 933888 z^3 - 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 ((11612160 + 3785985 z - 644400 z^2 + 62208 z^3 - 4096 z^4) Cos[2 Sqrt[z]] + 4 Sqrt[z] (5806080 - 3038805 z + 587184 z^2 - 59136 z^3 + 4096 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]