Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag21)

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`=-3/2

http://functions.wolfram.com/07.22.03.ag21.01

Input Form

HypergeometricPFQ[{21/4}, {-(3/2), -(23/4)}, -z] == (1 - (60 z)/23 + (3520 z^2)/1311 + (26624 z^3)/22287 - (32768 z^4)/35581 - (357302272 z^5)/1368978975 + (4194304 z^6)/392837445) Cos[2 Sqrt[z]] + (1/45176306175) (2 Sqrt[z] (45176306175 - 57616158600 z + 35026992000 z^2 + 51914649600 z^3 + 7677542400 z^4 + 2203582464 z^5 - 8388608 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]