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

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=9/2, a₂>=9/2

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

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

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

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(11/2), 6}, z] == (1/(7640325 z^3)) (32 E^(z/2) (329983453800 - 163027539675 z + 50586435900 z^2 - 11727431100 z^3 + 2185104600 z^4 - 341202960 z^5 + 45884160 z^6 - 5402880 z^7 + 545280 z^8 + 11520 z^9 + 132096 z^10 + 31744 z^11 + 2048 z^12) BesselI[0, z/2]) + (1/(7640325 z^4)) (32 E^(z/2) (-1319933815200 + 652110158700 z - 243593675325 z^2 + 67289121900 z^3 - 14635120500 z^4 + 2619129240 z^5 - 397862640 z^6 + 52496640 z^7 - 6132480 z^8 + 652800 z^9 - 79104 z^10 + 103424 z^11 + 29696 z^12 + 2048 z^13) 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]