Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7py)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a7py.01

Input Form

HypergeometricPFQ[{-(17/4)}, {1/2, 21/4}, z] == ((2 Sqrt[z] (13970023192125 - 22160994055200 z + 10744724390400 z^2 + 91854624153600 z^3 - 317747095142400 z^4 + 178969871646720 z^5 - 19880900296704 z^6 + 584652423168 z^7 - 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 + 3 (-23283371986875 + 53492054616000 z - 19266402355200 z^2 + 16372913356800 z^3 + 186981787238400 z^4 - 162409218048000 z^5 + 19375671214080 z^6 - 580894326784 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-69850115960625 + 11462583132000 z - 10638865036800 z^2 + 17784371404800 z^3 + 201431030169600 z^4 - 164621765836800 z^5 + 19446638837760 z^6 - 581431197696 z^7 + 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(100715515084800 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]