Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag3d)

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.ag3d.01

Input Form

HypergeometricPFQ[{21/4}, {-(1/2), -(23/4)}, -z] == (1/15058768725) ((15058768725 - 57616158600 z - 51459408000 z^2 + 39668428800 z^3 + 10770186240 z^4 + 1389887488 z^5 - 8388608 z^6) Cos[2 Sqrt[z]] - 2 Sqrt[z] (-15058768725 + 17459442000 z + 43243200000 z^2 + 3061555200 z^3 - 515440640 z^4 + 101711872 z^5) 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]