Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afy8)

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`=-9/2

http://functions.wolfram.com/07.22.03.afy8.01

Input Form

HypergeometricPFQ[{21/4}, {-(9/2), -(15/4)}, z] == (1 + (104 z)/45 + (688 z^2)/495 + (128 z^3)/231 + (16384 z^4)/51975 - (65536 z^5)/51975 - (13631488 z^6)/119282625 - (8388608 z^7)/32564156625) Cosh[2 Sqrt[z]] - (1/10854718875) (2 Sqrt[z] (10854718875 + 10613502900 z + 4795081200 z^2 + 1924715520 z^3 + 1710858240 z^4 + 3339714560 z^5 + 49283072 z^6) Sinh[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]