Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.7309)

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=3, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=3, b₁=6

http://functions.wolfram.com/07.25.03.7309.01

Input Form

HypergeometricPFQ[{-(7/2), 3}, {6, 6}, z] == (640 (32 - 136 z + 85 z^2))/(2431 z^5) + (1/(5584724145 z^5)) (1024 E^(z/2) (-45945900 + 218243025 z - 202001640 z^2 + 32932140 z^3 + 3854640 z^4 + 6694280 z^5 - 3417280 z^6 + 529696 z^7 - 32896 z^8 + 704 z^9) BesselI[0, z/2]) - (1/(5584724145 z^4)) (512 E^(z/2) (164390505 - 318524280 z + 79886160 z^2 + 13544080 z^3 + 7956800 z^4 - 5869632 z^5 + 995712 z^6 - 64384 z^7 + 1408 z^8) 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]
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