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

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=-9/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(9/2), 3}, z] == -((1/843908625) (8 E^(z/2) (-109289250 + 283854375 z - 451105200 z^2 + 673142400 z^3 - 1283688000 z^4 + 5980716000 z^5 + 22904985600 z^6 + 20541012480 z^7 + 8032919040 z^8 + 1620883200 z^9 + 179343360 z^10 + 10874880 z^11 + 335872 z^12 + 4096 z^13) BesselI[0, z/2])) - (1/(843908625 z)) (4 E^(z/2) (30405375 + 42099750 z - 241797150 z^2 + 432280800 z^3 - 624607200 z^4 + 995198400 z^5 - 2397729600 z^6 + 21413237760 z^7 + 28956890880 z^8 + 13301921280 z^9 + 2913753600 z^10 + 337920000 z^11 + 21090304 z^12 + 663552 z^13 + 8192 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]