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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=5/2

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

Input Form

HypergeometricPFQ[{19/4}, {5/2, -(21/4)}, z] == (1/(1929727800 z^(3/2))) (2 Sqrt[z] (-1839759075 - 2033262000 z + 1463616000 z^2 + 304128000 z^3 - 32440320 z^4 + 1048576 z^5) Cosh[2 Sqrt[z]] + 9 (204417675 + 605682000 z - 44352000 z^2 - 236544000 z^3 + 3604480 z^4 + 1048576 z^5) 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]