Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0993)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=11/2

http://functions.wolfram.com/07.22.03.0993.01

Input Form

HypergeometricPFQ[{-(9/2)}, {11/2, 11/2}, z] == (1/(4831838208 z^(9/2))) (2 Sqrt[z] (-3322946025 - 2697275700 z - 1326184650 z^2 - 753656400 z^3 + 347648526 z^4 - 26353656 z^5 + 650292 z^6 - 5824 z^7 + 16 z^8) Cosh[2 Sqrt[z]] + (-1177899975 - 2445357600 z - 1227492630 z^2 - 516310200 z^3 + 324522450 z^4 - 25734384 z^5 + 644556 z^6 - 5808 z^7 + 16 z^8) Sinh[2 Sqrt[z]] - 16 (-281302875 - 723350250 z - 578680200 z^2 - 300056400 z^3 - 225042300 z^4 + 90016920 z^5 - 6667920 z^6 + 163296 z^7 - 1458 z^8 + 4 z^9) SinhIntegral[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]