Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8504)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8504.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 7/4}, z] == ((4 z (551456539759125 - 429706394617500 z + 471449301523200 z^2 + 30598101212679000 z^3 - 28240149131251200 z^4 + 5073521935472640 z^5 - 289270535290880 z^6 + 6220744753152 z^7 - 51438944256 z^8 + 134217728 z^9) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (1654369619277375 - 974001161133000 z + 1152431625945600 z^2 + 9457151242839300 z^3 - 12745141589980800 z^4 + 2451299652172800 z^5 - 142733704888320 z^6 + 3094410428416 z^7 - 25677529088 z^8 + 67108864 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (4963108857832125 - 1976649415240500 z + 2851613483518800 z^2 - 10686184167859200 z^3 - 100350529292613600 z^4 + 108296913419735040 z^5 - 20014168369029120 z^6 + 1150940781477888 z^7 - 24831749783552 z^8 + 205621559296 z^9 - 536870912 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(92494595505312000 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]