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

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=7/2, a₂>=7/2

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

For fixed z and a₁=7/2, a₂=11/2, b₁=-5/2

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(5/2), 5}, z] == -((1/(70875 z^2)) (32 E^(z/2) (405405 - 218295 z + 68040 z^2 - 12600 z^3 - 3600 z^4 + 23472 z^5 + 65472 z^6 + 33216 z^7 + 5376 z^8 + 256 z^9) BesselI[0, z/2])) - (1/(70875 z^3)) (32 E^(z/2) (-1621620 + 873180 z - 331695 z^2 + 95760 z^3 - 23400 z^4 + 6912 z^5 - 6288 z^6 + 39552 z^7 + 28224 z^8 + 5120 z^9 + 256 z^10) 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]