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

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=9/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 9/2}, {-(11/2), 6}, z] == (1/(218295 z^3)) (32 E^(z/2) (21998896920 - 10344719385 z + 3101348250 z^2 - 695300760 z^3 + 125102880 z^4 - 18822384 z^5 + 2433312 z^6 - 275520 z^7 + 27648 z^8 - 2304 z^9 + 512 z^10) BesselI[0, z/2]) + (1/(218295 z^4)) (32 E^(z/2) (-87995587680 + 41378877540 z - 15155255115 z^2 + 4074320250 z^3 - 859458600 z^4 + 148742496 z^5 - 21783888 z^6 + 2761248 z^7 - 308160 z^8 + 30720 z^9 - 2816 z^10 + 512 z^11) 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]