Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anp9)

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=11/2, b₁>=-11/2

For fixed z and a₁=11/2, a₂=11/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.anp9.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(3/2), 4}, z] == (1/(893025 z)) (4 E^(z/2) (8505 + 224910 z - 1228500 z^2 + 10009440 z^3 + 55001520 z^4 + 68134752 z^5 + 34038144 z^6 + 8017920 z^7 + 930048 z^8 + 50688 z^9 + 1024 z^10) BesselI[0, z/2]) + (1/(893025 z^2)) (4 E^(z/2) (-34020 - 6615 z - 35910 z^2 + 313740 z^3 - 1522080 z^4 + 19947312 z^5 + 43704864 z^6 + 27271296 z^7 + 7160832 z^8 + 880896 z^9 + 49664 z^10 + 1024 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]
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]