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

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.afws.01

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), -(19/4)}, z] == (1 + (460 z)/209 + (2080 z^2)/1881 + (95168 z^3)/310365 + (17408 z^4)/241395 + (32768 z^5)/1206975 - (524288 z^6)/6517665 - (2512388096 z^7)/453727248975 - (67108864 z^8)/6805908734625) Cosh[2 Sqrt[z]] - (1/6805908734625) (2 Sqrt[z] (6805908734625 + 5904967068000 z + 2072527657200 z^2 + 501228000000 z^3 + 128314368000 z^4 + 82121195520 z^5 + 115715604480 z^6 + 1325400064 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]