Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8na)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a8na.01

Input Form

HypergeometricPFQ[{-(13/4)}, {3/2, 21/4}, z] == (17 (2 Sqrt[z] (-54784404675 + 94670175600 z - 63826963200 z^2 + 1578150604800 z^3 - 2294666035200 z^4 + 509428629504 z^5 - 24712839168 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 - 3 (-91307341125 + 222713290800 z - 120907987200 z^2 + 179891712000 z^3 - 1883647180800 z^4 + 488201256960 z^5 - 24477958144 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (273922023375 - 83772889200 z + 94962067200 z^2 - 290594304000 z^3 + 1936112025600 z^4 - 491158241280 z^5 + 24511512576 z^6 - 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (25178878771200 Sqrt[2] z^(15/4))

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]