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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(9/2), 1}, z] == (1/2679075) (E^(z/2) (2679075 - 9525600 z + 16669800 z^2 - 25137000 z^3 + 46683000 z^4 - 207990720 z^5 - 752451840 z^6 - 617025024 z^7 - 212260608 z^8 - 35850240 z^9 - 3090432 z^10 - 129024 z^11 - 2048 z^12) BesselI[0, z/2]) - (1/2679075) (4 E^(z/2) (-893025 z + 1951425 z^2 - 2929500 z^3 + 4602150 z^4 - 10710000 z^5 + 91840896 z^6 + 112557312 z^7 + 45168768 z^8 + 8236800 z^9 + 741120 z^10 + 31744 z^11 + 512 z^12) 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]