Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae3e)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=11/4, b_1`>=-11/2

For fixed z and a₁=11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.ae3e.01

Input Form

HypergeometricPFQ[{11/4}, {11/2, -(21/4)}, z] == (1/(2376192 z^(9/2))) (-2 Sqrt[z] (8649933917625 + 5323036257000 z + 865204623360 z^2 + 55819653120 z^3 + 1523515392 z^4 + 13107200 z^5) Cosh[2 Sqrt[z]] + (8649933917625 + 16856281480500 z + 4887054239760 z^2 + 488421964800 z^3 + 20673945600 z^4 + 341311488 z^5 + 1048576 z^6) 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]