Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al9k)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.al9k.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(9/2), 2}, z] == (1/1488375) (E^(z/2) (1488375 - 3231900 z + 4063500 z^2 - 4800600 z^3 + 7333200 z^4 - 27659520 z^5 - 85720320 z^6 - 56609280 z^7 - 14987520 z^8 - 1827840 z^9 - 101376 z^10 - 2048 z^11) BesselI[0, z/2]) + (1/1488375) (E^(z/2) (-467775 + 1606500 z - 2173500 z^2 + 2457000 z^3 - 3139920 z^4 + 6209280 z^5 - 46851840 z^6 - 44075520 z^7 - 13305600 z^8 - 1729536 z^9 - 99328 z^10 - 2048 z^11) 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]
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HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
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