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

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-7/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(7/2), -(23/4)}, z] == (1/(36727042275 z^(1/4))) (Sqrt[2] ((36727042275 - 66610536300 z + 12166308000 z^2 + 13950699840 z^3 + 4314562560 z^4 - 1006731264 z^5 + 3956277248 z^6 + 356515840 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (36727042275 - 17641146600 z - 20682723600 z^2 - 6884760960 z^3 - 1258414080 z^4 - 1801519104 z^5 + 1007681536 z^6 + 8388608 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (36727042275 + 31328243100 z + 11760764400 z^2 + 3101091840 z^3 + 1258414080 z^4 + 294649856 z^5 + 82837504 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]