Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj1l)

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=-7/2

http://functions.wolfram.com/07.25.03.aj1l.01

Input Form

HypergeometricPFQ[{5/2, 7/2}, {-(7/2), 6}, z] == (1/(315 z^3)) (32 E^(z/2) (-18378360 + 7162155 z - 1891890 z^2 + 370440 z^3 - 57120 z^4 + 7152 z^5 - 736 z^6 + 64 z^7) BesselI[0, z/2]) + (1/(315 z^4)) (32 E^(z/2) (73513440 - 28648620 z + 9864855 z^2 - 2376990 z^3 + 441000 z^4 - 65568 z^5 + 7984 z^6 - 800 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]