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

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {2, 2}, z] == (1/453600) (E^(z/2) (453600 + 3512880 z + 7399215 z^2 + 6410070 z^3 + 2660760 z^4 + 564000 z^5 + 61488 z^6 + 3232 z^7 + 64 z^8) BesselI[0, z/2]) + (1/453600) (E^(z/2) (10080 + 869940 z + 3692835 z^2 + 4434570 z^3 + 2179800 z^4 + 507168 z^5 + 58352 z^6 + 3168 z^7 + 64 z^8) 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]