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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=11/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(11/2), 4}, z] == (1/(49116375 z)) (4 E^(z/2) (103378275 - 31808700 z - 1871100 z^2 + 7597800 z^3 - 6350400 z^4 + 5080320 z^5 - 5564160 z^6 + 15828480 z^7 + 37912320 z^8 + 16481280 z^9 + 2669568 z^10 + 178176 z^11 + 4096 z^12) BesselI[0, z/2]) + (1/(49116375 z^2)) (4 E^(z/2) (-413513100 + 176351175 z - 72972900 z^2 + 27612900 z^3 - 10773000 z^4 + 5080320 z^5 - 3144960 z^6 + 2730240 z^7 - 4078080 z^8 + 24933120 z^9 + 14066688 z^10 + 2497536 z^11 + 174080 z^12 + 4096 z^13) 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]