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

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.agek.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), -(3/4)}, z] == (1/(186642225 z^(1/4))) (Sqrt[2] ((186642225 - 55301400 z - 1738044000 z^2 + 2520435456 z^3 - 1103542272 z^4 + 881295360 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (186642225 + 193554900 z - 766291680 z^2 - 308516544 z^3 + 377281536 z^4 + 88457216 z^5 + 262144 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (186642225 + 442411200 z + 537269040 z^2 - 447815424 z^3 + 156954624 z^4 + 3997696 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]