Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a987)

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`=11/2

http://functions.wolfram.com/07.22.03.a987.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 5/4}, -z] == (1/(246105600 z^(9/2))) (2 Sqrt[z] (42567525 - 1247400 z + 2661120 z^2 + 7096320 z^3 + 9860160 z^4 + 964608 z^5 + 16384 z^6) Cos[2 Sqrt[z]] + 64 Sqrt[Pi] z^(17/4) (3516975 + 2679600 z + 244992 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (42567525 - 58004100 z - 10810800 z^2 - 1774080 z^3 + 99348480 z^4 + 84331008 z^5 + 7815168 z^6 + 131072 z^7) 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]