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

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`=11/2

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

Input Form

HypergeometricPFQ[{3/4}, {11/2, 23/4}, -z] == (1/(33554432 z^(19/4))) (5985 (Sqrt[Pi] (12006225 - 17075520 z + 5322240 z^2 - 737280 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-1158885 + 342960 z - 46848 z^2 + 4096 z^3) Cos[2 Sqrt[z]] + (-1684305 + 390960 z - 49920 z^2 + 4096 z^3) 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]