Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.2672)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=1, b_1`>=-11/2

For fixed z and a₁=1, b₁=-11/2

http://functions.wolfram.com/07.22.03.2672.01

Input Form

HypergeometricPFQ[{1}, {-(11/2), 4}, -z] == (1/(13860 z^3)) (-135135 (255 + 30 z + 2 z^2) + 45 (765765 - 1441440 z + 336336 z^2 - 19712 z^3 + 256 z^4) Cos[2 Sqrt[z]] + 2 Sqrt[z] (34459425 - 18918900 z + 2162160 z^2 - 63360 z^3 + 256 z^4) 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]