Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amx0)

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=11/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.amx0.01

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(11/2), 6}, z] == (1/(68762925 z^3)) (32 E^(z/2) (-329983453800 + 166955914125 z - 52516163700 z^2 + 12328677900 z^3 - 2326401000 z^4 + 368595360 z^5 - 50803200 z^6 + 6531840 z^7 - 1175040 z^8 + 1440000 z^9 + 2970624 z^10 + 1029120 z^11 + 116736 z^12 + 4096 z^13) BesselI[0, z/2]) + (1/(68762925 z^4)) (32 E^(z/2) (1319933815200 - 667823656500 z + 251312586525 z^2 - 70175605500 z^3 + 15429714300 z^4 - 2790388440 z^5 + 427744800 z^6 - 56609280 z^7 + 6393600 z^8 - 437760 z^9 - 304896 z^10 + 2104320 z^11 + 918528 z^12 + 112640 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]