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

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{17/4}, {11/2, -(23/4)}, z] == (1/(479930880 z^(9/2))) (-10 Sqrt[z] (159177215822625 + 105008894991000 z + 20466141696000 z^2 + 1860558336000 z^3 + 95036178432 z^4 + 2801270784 z^5 + 33554432 z^6) Cosh[2 Sqrt[z]] + (795886079113125 + 1586225913772500 z + 519408291402000 z^2 + 66863815200000 z^3 + 4491002880000 z^4 + 176178462720 z^5 + 3612344320 z^6 + 16777216 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]