Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agj8)

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`=-3/2

http://functions.wolfram.com/07.22.03.agj8.01

Input Form

HypergeometricPFQ[{23/4}, {-(3/2), 21/4}, z] == (1/(143818752 Sqrt[2] z^(15/4))) (221 (2 Sqrt[z] (177161985 - 143256960 z - 59431680 z^2 - 9732096 z^3 - 2686976 z^4 + 524288 z^5) BesselI[1/4, Sqrt[z]]^2 + (-885809925 + 1346194080 z + 735356160 z^2 + 154091520 z^3 + 25362432 z^4 + 4194304 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-885809925 - 543533760 z - 136224000 z^2 - 22118400 z^3 - 3866624 z^4 + 524288 z^5) 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]