Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9q0)

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`=-11/2

http://functions.wolfram.com/07.22.03.a9q0.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(11/2), 23/4}, z] == (19 (2 Sqrt[z] (-53059071940875 - 51666348333600 z - 3945934137600 z^2 - 77178716160 z^3 + 10605494272 z^4 + 903872512 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 + (159177215822625 + 397554802444800 z + 76662755769600 z^2 + 2447667855360 z^3 - 4328325120 z^4 - 914358272 z^5 - 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (159177215822625 + 57976742023200 z + 4724267708160 z^2 + 22899179520 z^3 + 10838016000 z^4 + 908066816 z^5 + 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (251255586816 Sqrt[2] z^(17/4))

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]