Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8942)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8942.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 13/4}, z] == ((2 Sqrt[z] (8538321867075 + 2711726380162800 z - 4614321637981440 z^2 + 1625677143552000 z^3 - 164064626933760 z^4 + 5713091887104 z^5 - 71521271808 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 - 3 (14230536445125 + 318764016370800 z - 3401424490464000 z^2 + 1490107002531840 z^3 - 159169518305280 z^4 + 5650907136000 z^5 - 71286390784 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (42691609335375 + 469375411705200 z - 3540962686060800 z^2 + 1508043361628160 z^3 - 159849402531840 z^4 + 5659715174400 z^5 - 71319945216 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(2514396274790400 Sqrt[2] z^(7/4))

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]