Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a89o)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a89o.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, 11/4}, z] == ((2 z (5262000975 + 63244011600 z - 38760076800 z^2 + 4411760640 z^3 - 135331840 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (13480807725 + 45018666000 z - 36217843200 z^2 + 4328939520 z^3 - 134676480 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 (1728896400 + 11876339475 z + 55047762000 z^2 - 37708070400 z^3 + 4378337280 z^4 - 135069696 z^5 + 1048576 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (88216128000 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]