Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0547)

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/07.22.03.0547.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3/2, 3/2}, z] == (1/(33177600 Sqrt[z])) (-2 Sqrt[z] (-8262405 + 8640990 z - 1620936 z^2 + 88320 z^3 - 1580 z^4 + 8 z^5) Cosh[2 Sqrt[z]] + (4584195 - 7415550 z + 1540800 z^2 - 86784 z^3 + 1572 z^4 - 8 z^5) Sinh[2 Sqrt[z]] + 8 (467775 - 5613300 z + 4677750 z^2 - 831600 z^3 + 44550 z^4 - 792 z^5 + 4 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]