Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agq3)

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`=9/2

http://functions.wolfram.com/07.22.03.agq3.01

Input Form

HypergeometricPFQ[{23/4}, {9/2, -(21/4)}, -z] == (1/(16761064320 z^(7/2))) (2 Sqrt[z] (3326897660625 - 2560126961700 z + 719550216000 z^2 - 131459328000 z^3 + 2568192000 z^4 + 2693529600 z^5 + 4194304 z^6) Cos[2 Sqrt[z]] + (-3326897660625 + 6995990509200 z - 2950155885600 z^2 + 639600192000 z^3 - 80898048000 z^4 - 10164633600 z^5 + 1096810496 z^6 + 33554432 z^7) 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]