Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.4844)

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/07.22.03.4844.01

Input Form

HypergeometricPFQ[{9/2}, {-(11/2), -(9/2)}, z] == (1 + (24 z)/11 + (736 z^2)/693 + (4096 z^3)/14553 + (512 z^4)/8085 + (4096 z^5)/155925 - (16384 z^6)/467775 - (65536 z^7)/68762925) Cosh[2 Sqrt[z]] - (1/1031443875) (2 Sqrt[z] (1031443875 + 875164500 z + 295293600 z^2 + 68040000 z^3 + 16934400 z^4 + 13547520 z^5 + 4915200 z^6 + 16384 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]