Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a91s)

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

For fixed z and a₁=-11/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a91s.01

Input Form

HypergeometricPFQ[{-(11/4)}, {1/2, 15/4}, z] == (1/(132710400 Sqrt[2] z^(9/4))) ((-2 Sqrt[z] (3274425 - 831600 z - 59788800 z^2 + 181002240 z^3 - 35848192 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]]^2 + (9823275 + 12474000 z + 5322240 z^2 + 160358400 z^3 - 35192832 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (-9823275 + 8482320 z - 26611200 z^2 + 172449792 z^3 - 35586048 z^4 + 1048576 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]