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

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`=-11/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), -(15/4)}, z] == (1 + (124 z)/55 + (6752 z^2)/5445 + (4288 z^3)/10395 + (4096 z^4)/27225 - (32768 z^5)/571725 + (1048576 z^6)/8575875 + (4194304 z^7)/2436773625) Cosh[2 Sqrt[z]] + (1/358205722875) (2 Sqrt[z] (-358205722875 - 329983453800 z - 131572350000 z^2 - 41140794240 z^3 - 20530298880 z^4 + 41060597760 z^5 + 4017094656 z^6 + 8388608 z^7) 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]