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

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.ageg.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), -(7/4)}, z] == -((1/(1306495575 z^(1/4))) (Sqrt[2] ((-1306495575 + 1659042000 z - 189604800 z^2 + 6471843840 z^3 - 12400012800 z^4 + 14475091968 z^5 + 992870400 z^6 + 2097152 z^7) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-435498525 - 27650700 z + 10533600 z^2 + 1145148480 z^3 + 41149440 z^4 + 856866816 z^5 + 12320768 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-1306495575 - 1824946200 z - 2069852400 z^2 - 1960479360 z^3 + 1853245440 z^4 + 220889088 z^5 + 524288 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]