Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2559)

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=5, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5, b₁=5

http://functions.wolfram.com/07.25.03.2559.01

Input Form

HypergeometricPFQ[{-(11/2), 5}, {5, 5}, z] == (1/(218243025 z^2)) (32 E^(z/2) (31185 + 83160 z + 6985440 z^2 - 10478160 z^3 + 5331360 z^4 - 1212096 z^5 + 132864 z^6 - 6784 z^7 + 128 z^8) BesselI[0, z/2]) - (1/(218243025 z^3)) (128 E^(z/2) (31185 + 83160 z + 166320 z^2 + 436590 z^3 - 1654080 z^4 + 1074804 z^5 - 272256 z^6 + 31568 z^7 - 1664 z^8 + 32 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]