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

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`=-7/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(7/2), -(15/4)}, z] == (1 + (12 z)/5 + (272 z^2)/165 + (1024 z^3)/1155 + (8192 z^4)/5775 + (79691776 z^5)/34459425 + (19922944 z^6)/516891375) Cosh[2 Sqrt[z]] + (1/3618239625) (2 Sqrt[z] (-3618239625 - 3859455600 z - 2105157600 z^2 - 1283143680 z^3 + 8173240320 z^4 + 825753600 z^5 + 2097152 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]