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

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(11/2), -(13/4)}, z] == (1/1404728325) (77 (18243225 + 40313700 z + 20714400 z^2 + 6361920 z^3 + 2903040 z^4 + 1032192 z^5 + 262144 z^6) Cosh[2 Sqrt[z]] + 2 Sqrt[z] (-1404728325 - 1231183800 z - 452889360 z^2 - 133499520 z^3 - 115906560 z^4 + 52985856 z^5 + 524288 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]