Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag8p)

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.ag8p.01

Input Form

HypergeometricPFQ[{21/4}, {7/2, -(23/4)}, -z] == (1/(32125373280 z^(5/2))) (2 Sqrt[z] (314786847375 - 279810531000 z + 140851751040 z^2 - 47048601600 z^3 + 333971456 z^5 + 8388608 z^6) Cos[2 Sqrt[z]] + (-314786847375 + 699526327500 z - 385945560000 z^2 + 192899266560 z^3 - 25092587520 z^4 - 2361655296 z^5 + 20971520 z^6) 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]