Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj0h)

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=-11/2

http://functions.wolfram.com/07.25.03.aj0h.01

Input Form

HypergeometricPFQ[{5/2, 7/2}, {-(11/2), 5}, z] == (1/(155925 z^2)) (32 E^(z/2) (-654729075 + 310134825 z - 93555000 z^2 + 21115080 z^3 - 3828240 z^4 + 581040 z^5 - 75840 z^6 + 8640 z^7 - 768 z^8 + 256 z^9) BesselI[0, z/2]) + (1/(155925 z^3)) (32 E^(z/2) (2618916300 - 1240539300 z + 456080625 z^2 - 123243120 z^3 + 26161560 z^4 - 4561920 z^5 + 674160 z^6 - 86400 z^7 + 9792 z^8 - 1024 z^9 + 256 z^10) 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]