Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajo6)

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=-7/2

http://functions.wolfram.com/07.25.03.ajo6.01

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(7/2), 4}, z] == (1/(99225 z)) (4 E^(z/2) (-405405 + 266490 z - 113400 z^2 + 50400 z^3 - 39600 z^4 + 103968 z^5 + 244416 z^6 + 99840 z^7 + 13056 z^8 + 512 z^9) BesselI[0, z/2]) + (1/(99225 z^2)) (4 E^(z/2) (1621620 - 966735 z + 357210 z^2 - 88200 z^3 + 7200 z^4 + 12528 z^5 - 25824 z^6 + 162624 z^7 + 87552 z^8 + 12544 z^9 + 512 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]