Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5491)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=11/2, b₁=1/2

http://functions.wolfram.com/07.25.03.5491.01

Input Form

HypergeometricPFQ[{-(9/2), 11/2}, {1/2, 5}, z] == -((1/(11486475 z^2)) (32 E^(z/2) (-315 + 540 z - 359910 z^2 + 3737160 z^3 - 6065280 z^4 + 3144192 z^5 - 581632 z^6 + 32768 z^7) BesselI[0, z/2])) + (1/(11486475 z^3)) (64 E^(z/2) (-630 + 1080 z - 1935 z^2 + 8145 z^3 + 450660 z^4 - 1847616 z^5 + 1305856 z^6 - 274432 z^7 + 16384 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]