Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajn7)

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=-11/2

http://functions.wolfram.com/07.25.03.ajn7.01

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(11/2), 3}, z] == (1/29469825) (16 E^(z/2) (3742200 - 2962575 z + 1701000 z^2 - 992250 z^3 + 705600 z^4 - 745920 z^5 + 2096640 z^6 + 4983936 z^7 + 2138112 z^8 + 341760 z^9 + 22528 z^10 + 512 z^11) BesselI[0, z/2]) + (1/(29469825 z)) (4 E^(z/2) (-30405375 + 8108100 z + 1474200 z^2 - 2835000 z^3 + 2205000 z^4 - 1612800 z^5 + 1451520 z^6 - 2167296 z^7 + 13179648 z^8 + 7314432 z^9 + 1280000 z^10 + 88064 z^11 + 2048 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]