Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8416)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8416.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 15/4}, z] == ((2 Sqrt[z] (52961313136606875 + 261032311183644000 z + 2345810300587353600 z^2 - 1542320547487948800 z^3 + 227187769009766400 z^4 - 11391690772316160 z^5 + 223916945571840 z^6 - 1732482433024 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 - (158883939409820625 + 597758426889624000 z + 1660429473320217600 z^2 - 1417113478106726400 z^3 + 220424588712345600 z^4 - 11254602745774080 z^5 + 222841358254080 z^6 - 1729798078464 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (161701585625955375 + 510599237270522400 z + 2031647156675136000 z^2 - 1489592174592614400 z^3 + 224424204750028800 z^4 - 11336380380610560 z^5 + 223485502685184 z^6 - 1731408691200 z^7 + 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(3256572466667520000 Sqrt[2] z^(9/4))

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]