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

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=11/2, a₂>=11/2

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

For fixed z and a₁=11/2, a₂=11/2, b₁=-1/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(1/2), 2}, z] == (1/893025) (E^(z/2) (893025 - 27452250 z - 367351740 z^2 - 983193120 z^3 - 1037831760 z^4 - 528625440 z^5 - 142007040 z^6 - 20846592 z^7 - 1656576 z^8 - 66048 z^9 - 1024 z^10) BesselI[0, z/2]) + (1/893025) (E^(z/2) (-33075 + 1869210 z - 68641020 z^2 - 438893280 z^3 - 671060880 z^4 - 413411040 z^5 - 123455232 z^6 - 19286016 z^7 - 1592064 z^8 - 65024 z^9 - 1024 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]
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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]