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

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.amlf.01

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(11/2), 1}, z] == (1/114604875) (E^(z/2) (114604875 - 479256750 z + 885020850 z^2 - 1226685600 z^3 + 1700848800 z^4 - 3097886400 z^5 + 13980254400 z^6 + 52242140160 z^7 + 45600387840 z^8 + 17409262080 z^9 + 3440478720 z^10 + 373882880 z^11 + 22319104 z^12 + 679936 z^13 + 8192 z^14) BesselI[0, z/2]) + (1/114604875) (2 E^(z/2) (84473550 z - 208339425 z^2 + 306406800 z^3 - 404409600 z^4 + 611352000 z^5 - 1423487520 z^6 + 12425656320 z^7 + 16194286080 z^8 + 7233891840 z^9 + 1549049600 z^10 + 176279552 z^11 + 10825728 z^12 + 335872 z^13 + 4096 z^14) 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]