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

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=11/2, b₁>=-11/2

For fixed z and a₁=11/2, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(7/2), 1}, z] == (1/93767625) (E^(z/2) (93767625 - 857304000 z + 3790593450 z^2 - 15758404200 z^3 + 135132066720 z^4 + 869820819840 z^5 + 1372794091200 z^6 + 965985108480 z^7 + 361163577600 z^8 + 77752313856 z^9 + 10000323072 z^10 + 772638720 z^11 + 34811904 z^12 + 835584 z^13 + 8192 z^14) BesselI[0, z/2]) + (1/93767625) (2 E^(z/2) (89004825 z - 540110025 z^2 + 2109682260 z^3 - 9666125280 z^4 + 138615533280 z^5 + 388406884320 z^6 + 348343752960 z^7 + 148173193728 z^8 + 34406436096 z^9 + 4638729984 z^10 + 369527808 z^11 + 16994304 z^12 + 413696 z^13 + 4096 z^14) 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]