Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.4842)

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/07.22.03.4842.01

Input Form

HypergeometricPFQ[{9/2}, {-(11/2), -(11/2)}, z] == (1/11345882625) ((11345882625 + 24379582500 z + 11168766000 z^2 + 2632694400 z^3 + 468115200 z^4 + 94832640 z^5 + 90316800 z^6 + 22609920 z^7 + 65536 z^8) Cosh[2 Sqrt[z]] + 2 Sqrt[z] (-11345882625 - 9251739000 z - 2867205600 z^2 - 562464000 z^3 - 99187200 z^4 - 27095040 z^5 + 45957120 z^6 + 1048576 z^7) Sinh[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]