Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agi3)

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`=-3/2

http://functions.wolfram.com/07.22.03.agi3.01

Input Form

HypergeometricPFQ[{23/4}, {-(3/2), -(21/4)}, -z] == (1/41247931725) ((41247931725 - 112613400900 z + 135567432000 z^2 - 192601221120 z^3 - 96396410880 z^4 - 31324372992 z^5 + 574619648 z^6) Cos[2 Sqrt[z]] - 2 Sqrt[z] (-41247931725 + 57616158600 z - 110719889280 z^2 + 3023032320 z^3 + 14922547200 z^4 - 3403153408 z^5 + 8388608 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]