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

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`=-5/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(5/2), -(21/4)}, -z] == (1/206239658625) ((206239658625 - 502831929600 z + 366032066400 z^2 - 250278336000 z^3 + 301281361920 z^4 + 216312053760 z^5 - 17634951168 z^6 + 33554432 z^7) Cos[2 Sqrt[z]] + 6 Sqrt[z] (68746552875 - 75948572700 z + 45189144000 z^2 - 62185052160 z^3 - 12235407360 z^4 - 17247764480 z^5 + 213909504 z^6) Sin[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]