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

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-7/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(7/2), -(19/4)}, z] == (1 + (44 z)/19 + (80 z^2)/57 + (1792 z^3)/3135 + (8192 z^4)/21945 - (702414848 z^5)/654729075 - (208666624 z^6)/1964187225 - (16777216 z^7)/68746552875) Cosh[2 Sqrt[z]] - (1/1964187225) (2 Sqrt[z] (1964187225 + 1929727800 z + 882161280 z^2 + 366612480 z^3 + 59768832 z^4 + 548929536 z^5 + 8388608 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]