Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a88k)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-21/4, b>=a

For fixed z and a=-21/4, b=-15/4

http://functions.wolfram.com/07.23.03.a88k.01

Input Form

Hypergeometric2F1[-(21/4), -(15/4), 5, -z] == (1/(166966608033225 Pi z^4)) (4096 (1 + z)^(1/4) (4 (-297024 - 7041944 z - 97512051 z^2 - 1355260179 z^3 + 65771178813 z^4 - 197553658203 z^5 + 150821670447 z^6 - 30364343457 z^7 + 910642887 z^8 + 9388071 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-594048 - 13638352 z - 184864953 z^2 - 2573443782 z^3 + 51924698505 z^4 - 108237934116 z^5 + 54788353641 z^6 - 5976301926 z^7 + 9388071 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - 2 (-297024 - 7041944 z - 97512051 z^2 - 1355260179 z^3 + 65771178813 z^4 - 197553658203 z^5 + 150821670447 z^6 - 30364343457 z^7 + 910642887 z^8 + 9388071 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))

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,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]