Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1536)

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=5/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.1536.01

Input Form

HypergeometricPFQ[{-(11/2), 5/2}, {-(3/2), 5}, z] == (1/(130945815 z^2)) (32 E^(z/2) (7203735 + 2619540 z + 3575880 z^2 + 4906440 z^3 + 15656184 z^4 - 39820800 z^5 + 18244608 z^6 - 2654208 z^7 + 114688 z^8) BesselI[0, z/2]) - (1/(130945815 z^3)) (128 E^(z/2) (7203735 + 2619540 z - 291060 z^2 - 467775 z^3 - 560016 z^4 - 964290 z^5 - 6303360 z^6 + 3940608 z^7 - 634880 z^8 + 28672 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]