Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0563)

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

For fixed z and a₁=-11/2, b₁=3/2

http://functions.wolfram.com/07.22.03.0563.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3/2, 11/2}, z] == (1/(5662310400 z^(9/2))) (-2 Sqrt[z] (-147349125 + 42099750 z - 52390800 z^2 + 157172400 z^3 - 836755650 z^4 + 252719820 z^5 - 19698840 z^6 + 531984 z^7 - 5272 z^8 + 16 z^9) Cosh[2 Sqrt[z]] + (-147349125 - 154365750 z + 56133000 z^2 + 52390800 z^3 + 664552350 z^4 - 235632780 z^5 + 19194840 z^6 - 526800 z^7 + 5256 z^8 - 16 z^9) Sinh[2 Sqrt[z]] + 32 z^4 (49116375 - 117879300 z + 32744250 z^2 - 2494800 z^3 + 66825 z^4 - 660 z^5 + 2 z^6) 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]