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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(11/2), -(13/4)}, z] == (1 + (332 z)/143 + (608 z^2)/429 + (26176 z^3)/45045 + (4096 z^4)/9009 + (32768 z^5)/289575 + (1048576 z^6)/6081075 + (4194304 z^7)/2426348925) Cosh[2 Sqrt[z]] + (1/400347572625) (2 Sqrt[z] (-400347572625 - 395681517000 z - 182162811600 z^2 - 76221129600 z^3 - 113257267200 z^4 + 90605813760 z^5 + 5206179840 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]