Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aey2)

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aey2.01

Input Form

HypergeometricPFQ[{15/4}, {9/2, -(21/4)}, z] == (1/(58810752 z^(7/2))) (-6 Sqrt[z] (221793177375 + 150396897420 z + 31398554880 z^2 + 3265726464 z^3 + 200409088 z^4 + 4980736 z^5) Cosh[2 Sqrt[z]] + (665379532125 + 1338363401760 z + 459203865120 z^2 + 65122928640 z^3 + 5211537408 z^4 + 224919552 z^5 + 2097152 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]