Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9r3)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a9r3.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(9/2), 13/4}, -z] == (1/(100663296 z^(9/4))) (11 Sqrt[Pi] (18583425 + 8809920 z + 9192960 z^2 - 1720320 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((204417675 - 121136400 z + 2797824 z^2 - 45056 z^3) Cos[2 Sqrt[z]] + 44 Sqrt[z] (6194475 + 104880 z - 108288 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]