Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1977)

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=7/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=7/2, b₁=5/2

http://functions.wolfram.com/07.25.03.1977.01

Input Form

HypergeometricPFQ[{-(11/2), 7/2}, {5/2, 5}, z] == (1/(1091215125 z^2)) (32 E^(z/2) (-93555 - 51975 z + 34345080 z^2 - 68108040 z^3 + 44120400 z^4 - 12300912 z^5 + 1604160 z^6 - 95168 z^7 + 2048 z^8) BesselI[0, z/2]) - (1/(1091215125 z^3)) (32 E^(z/2) (-374220 - 207900 z + 966735 z^2 + 5821200 z^3 - 38320680 z^4 + 33956352 z^5 - 10833360 z^6 + 1512064 z^7 - 93120 z^8 + 2048 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]