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

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=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 9/2}, {-(7/2), 6}, z] == (1/(2205 z^3)) (32 E^(z/2) (55135080 - 25540515 z + 7567560 z^2 - 1675800 z^3 + 297360 z^4 - 44016 z^5 + 5568 z^6 - 576 z^7 + 128 z^8) BesselI[0, z/2]) + (1/(2205 z^4)) (32 E^(z/2) (-220540320 + 102162060 z - 37162125 z^2 + 9896040 z^3 - 2063880 z^4 + 352464 z^5 - 50832 z^6 + 6336 z^7 - 704 z^8 + 128 z^9) 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]