Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj0t)

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=7/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=7/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.aj0t.01

Input Form

HypergeometricPFQ[{5/2, 7/2}, {-(9/2), 2}, z] == (1/42525) (E^(z/2) (42525 - 54810 z + 44280 z^2 - 36000 z^3 + 39600 z^4 - 110880 z^5 - 256704 z^6 - 101376 z^7 - 13056 z^8 - 512 z^9) BesselI[0, z/2]) + (1/42525) (E^(z/2) (-31185 + 40230 z - 29880 z^2 + 21600 z^3 - 19440 z^4 + 28896 z^5 - 173376 z^6 - 89088 z^7 - 12544 z^8 - 512 z^9) 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]