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

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=-7/2

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

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(7/2), 3}, z] == (1/1157625) (4 E^(z/2) (312795 - 687960 z + 1064700 z^2 - 1915200 z^3 + 8079120 z^4 + 27299328 z^5 + 20057856 z^6 + 5867520 z^7 + 783104 z^8 + 47104 z^9 + 1024 z^10) BesselI[0, z/2]) + (1/(1157625 z)) (4 E^(z/2) (-93555 - 59535 z + 303660 z^2 - 497700 z^3 + 771120 z^4 - 1719312 z^5 + 14036736 z^6 + 15231744 z^7 + 5152000 z^8 + 737536 z^9 + 46080 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]