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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(11/2), 5}, z] == (1/(9823275 z^2)) (32 E^(z/2) (654729075 - 379053675 z + 130353300 z^2 - 33056100 z^3 + 6728400 z^4 - 1164240 z^5 + 188160 z^6 - 42240 z^7 + 49920 z^8 + 87296 z^9 + 19456 z^10 + 1024 z^11) BesselI[0, z/2]) + (1/(9823275 z^3)) (32 E^(z/2) (-2618916300 + 1516214700 z - 602026425 z^2 + 178378200 z^3 - 41674500 z^4 + 7983360 z^5 - 1281840 z^6 + 168960 z^7 - 11520 z^8 - 11264 z^9 + 69376 z^10 + 18432 z^11 + 1024 z^12) 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]