Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.age7)

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.age7.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), -(17/4)}, -z] == (1 - (352 z)/153 + (18896 z^2)/13923 - (21248 z^3)/41769 + (8192 z^4)/36855 - (131072 z^5)/149175 + (10828644352 z^6)/41247931725 - (16777216 z^7)/7279046775) Cos[2 Sqrt[z]] + (1/618718975875) (2 Sqrt[z] (618718975875 - 598499401500 z + 261702025200 z^2 - 94802400000 z^3 + 56628633600 z^4 + 261411962880 z^5 - 11245977600 z^6 + 16777216 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]