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

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=-5/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(5/2), 5}, z] == -((1/(4465125 z^2)) (32 E^(z/2) (-405405 + 155925 z - 192780 z^2 + 409500 z^3 - 932400 z^4 + 4577328 z^5 + 17230080 z^6 + 14254848 z^7 + 4633344 z^8 + 677120 z^9 + 44032 z^10 + 1024 z^11) BesselI[0, z/2])) - (1/(4465125 z^3)) (32 E^(z/2) (1621620 - 623700 z + 263655 z^2 - 27720 z^3 - 144900 z^4 + 338688 z^5 - 905520 z^6 + 8212992 z^7 + 10513152 z^8 + 4019200 z^9 + 634624 z^10 + 43008 z^11 + 1024 z^12) 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]