Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa2w)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aa2w.01

Input Form

HypergeometricPFQ[{-(7/4)}, {9/2, 7/4}, z] == (1/(636480 Sqrt[2] z^(11/4))) ((4 z (-11025 + 10080 z + 238800 z^2 - 94720 z^3 + 4096 z^4) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-33075 + 23940 z + 93240 z^2 - 46080 z^3 + 2048 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (99225 - 52920 z + 161280 z^2 + 866880 z^3 - 374784 z^4 + 16384 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

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]