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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), -(21/4)}, -z] == (1/7522320180375) ((7522320180375 - 16282078312500 z + 7675776108000 z^2 - 1902444667200 z^3 + 368032896000 z^4 - 88221450240 z^5 + 190749081600 z^6 - 27619491840 z^7 + 67108864 z^8) Cos[2 Sqrt[z]] + 6 Sqrt[z] (2507440060125 - 2084106024000 z + 671318247600 z^2 - 140440608000 z^3 + 27675648000 z^4 - 9537454080 z^5 - 21920481280 z^6 + 385875968 z^7) Sin[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]