Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af29)

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.af29.01

Input Form

HypergeometricPFQ[{17/4}, {-(9/2), -(15/4)}, -z] == (1 - (304 z)/135 + (368 z^2)/297 - (13312 z^3)/31185 + (8192 z^4)/42525 + (262144 z^5)/467775 - (1048576 z^6)/39092625) Cos[2 Sqrt[z]] + (1/1915538625) (2 Sqrt[z] (1915538625 - 1759457700 z + 708598800 z^2 - 239016960 z^3 + 167731200 z^4 - 201850880 z^5 + 1048576 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]