Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9758)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9758.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(9/2), 13/4}, z] == ((-2 Sqrt[z] (-406586755575 - 69288579360 z + 505235808000 z^2 + 119923752960 z^3 + 11264262144 z^4 + 568328192 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (-677644592625 + 1606268664000 z + 631731260160 z^2 + 130729082880 z^3 + 11786321920 z^4 + 583008256 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-2032933777875 + 481880599200 z + 608384874240 z^2 + 128981975040 z^3 + 11707023360 z^4 + 580911104 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(743921418240 Sqrt[2] z^(7/4))

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]