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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{23/4}, {11/2, -(21/4)}, -z] == (1/(7449361920 z^(9/2))) (-2 Sqrt[z] (181648612270125 - 127752870168000 z + 28997873704800 z^2 - 3453841036800 z^3 + 285839769600 z^4 - 14269808640 z^5 - 723517440 z^6 + 33554432 z^7) Cos[2 Sqrt[z]] + (181648612270125 - 369951019861500 z + 134748860677200 z^2 - 21298686393600 z^3 + 2046720614400 z^4 - 146695127040 z^5 + 1368391680 z^6 + 520093696 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]