Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag0p)

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`=-5/2

http://functions.wolfram.com/07.22.03.ag0p.01

Input Form

HypergeometricPFQ[{21/4}, {-(5/2), -(23/4)}, -z] == (1/225881530875) ((225881530875 - 534258925200 z + 351761810400 z^2 - 194075481600 z^3 - 82844467200 z^4 + 28244705280 z^5 - 12190744576 z^6 + 33554432 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (225881530875 - 233083550700 z + 121297176000 z^2 - 49861785600 z^3 - 72314880000 z^4 - 25012469760 z^5 + 549453824 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]