Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8028)

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`=-9/2

http://functions.wolfram.com/07.22.03.8028.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 11/4}, z] == -(((2 Sqrt[z] (-7905853580625 - 20297655378000 z - 15126707232000 z^2 - 3360099225600 z^3 - 397585612800 z^4 - 33108787200 z^5 - 2936012800 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 + (23717560741875 + 25298731458000 z + 17817063264000 z^2 + 3656456294400 z^3 + 420087398400 z^4 + 34492907520 z^5 + 2768240640 z^6 - 268435456 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (-23717560741875 + 25298731458000 z + 16149259526400 z^2 + 3472829337600 z^3 + 406515548160 z^4 + 33737932800 z^5 + 2868903936 z^6 - 268435456 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(47823519744000 Sqrt[2] z^(5/4)))

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]