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

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=1/4, b_1`>=-11/2

For fixed z and a₁=1/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{1/4}, {-(11/2), 21/4}, -z] == (221 (504735 Sqrt[Pi] (668365425 + 84369600 z + 6428160 z^2 + 442368 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (9 (37483046976375 - 35250328990800 z + 5467612550400 z^2 - 214069309440 z^3 + 1744830464 z^4) Cos[2 Sqrt[z]] + 4 Sqrt[z] (112449140929125 - 37210558215600 z + 2900401862400 z^2 - 52919930880 z^3 + 134217728 z^4) Sin[2 Sqrt[z]])))/ (3968549781504 z^(17/4))

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]