Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2738)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=11/2, b₁=3/2

http://functions.wolfram.com/07.25.03.2738.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {3/2, 5}, z] == (1/(3273645375 z^2)) (32 E^(z/2) (-7425 + 17820 z + 102243240 z^2 - 462864600 z^3 + 573026040 z^4 - 277418880 z^5 + 58349568 z^6 - 5259264 z^7 + 163840 z^8) BesselI[0, z/2]) - (1/(3273645375 z^3)) (128 E^(z/2) (-7425 + 17820 z - 58410 z^2 + 902385 z^3 - 41977800 z^4 + 92160990 z^5 - 56616672 z^6 + 13334016 z^7 - 1273856 z^8 + 40960 z^9) 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]