Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ala5)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=9/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.ala5.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(7/2), 4}, z] == (1/(55125 z)) (4 E^(z/2) (135135 - 45990 z - 2520 z^2 + 16800 z^3 - 25200 z^4 + 78624 z^5 + 193984 z^6 + 84992 z^7 + 12032 z^8 + 512 z^9) BesselI[0, z/2]) + (1/(55125 z^2)) (4 E^(z/2) (-540540 + 239085 z - 96390 z^2 + 36120 z^3 - 16800 z^4 + 13104 z^5 - 19936 z^6 + 125504 z^7 + 73728 z^8 + 11520 z^9 + 512 z^10) BesselI[1, z/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},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},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]