Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.3341)

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=2, b_1`>=-11/2

For fixed z and a₁=2, b₁=-9/2

http://functions.wolfram.com/07.22.03.3341.01

Input Form

HypergeometricPFQ[{2}, {-(9/2), 6}, -z] == (1/(126 z^5)) (45045 (29070 + 2295 z + 90 z^2 + 2 z^3) + (-1309458150 + 2515538025 z - 670269600 z^2 + 55495440 z^3 - 1647360 z^4 + 13568 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-1309458150 + 769593825 z - 109729620 z^2 + 5456880 z^3 - 91520 z^4 + 256 z^5) 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]