Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajn5)

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=-11/2

http://functions.wolfram.com/07.25.03.ajn5.01

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(11/2), 2}, z] == (1/29469825) (E^(z/2) (29469825 - 48024900 z + 44055900 z^2 - 35721000 z^3 + 32104800 z^4 - 40561920 z^5 + 132652800 z^6 + 365062656 z^7 + 204164352 z^8 + 45941760 z^9 + 4809728 z^10 + 231424 z^11 + 4096 z^12) BesselI[0, z/2]) + (1/29469825) (E^(z/2) (-14189175 + 28973700 z - 27386100 z^2 + 21609000 z^3 - 17892000 z^4 + 18627840 z^5 - 31874304 z^6 + 217093632 z^7 + 164775168 z^8 + 41466880 z^9 + 4584448 z^10 + 227328 z^11 + 4096 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]