Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a81s)

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`=-5/2

http://functions.wolfram.com/07.22.03.a81s.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(5/2), 15/4}, z] == -(((2 Sqrt[z] (5065535475 + 2205403200 z - 4341392640 z^2 - 2568683520 z^3 - 567214080 z^4 - 104857600 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 + (-15196606425 - 29772943200 z + 5500535040 z^2 + 2904145920 z^3 + 604569600 z^4 + 94371840 z^5 - 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (15196606425 - 2646483840 z + 5085400320 z^2 + 2720563200 z^3 + 586874880 z^4 + 100663296 z^5 - 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (9201254400 Sqrt[2] z^(9/4)))

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]