Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.4215)

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=7/2, b_1`>=-11/2

For fixed z and a₁=7/2, b₁=-11/2

http://functions.wolfram.com/07.22.03.4215.01

Input Form

HypergeometricPFQ[{7/2}, {-(11/2), -(11/2)}, -z] == (1/1620840375) (-21 (-77182875 + 163296000 z - 70308000 z^2 + 14947200 z^3 - 2280960 z^4 + 368640 z^5 - 245760 z^6 + 32768 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (1620840375 - 1268095500 z + 361972800 z^2 - 62596800 z^3 + 9192960 z^4 - 1935360 z^5 - 2039808 z^6 + 16384 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]