Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ae69)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=1/2, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ae69.01

Input Form

HypergeometricPFQ[{1/2, 11/2}, {-(11/2), 3}, z] == (1/9823275) (8 E^(z/2) (2494800 - 2338875 z + 1134000 z^2 - 378000 z^3 + 100800 z^4 - 28080 z^5 + 24960 z^6 + 36864 z^7 + 6144 z^8 + 256 z^9) BesselI[0, z/2]) + (1/(9823275 z)) (4 E^(z/2) (-10135125 + 12162150 z - 7512750 z^2 + 3024000 z^3 - 882000 z^4 + 194400 z^5 - 28320 z^6 - 6912 z^7 + 62208 z^8 + 11776 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]